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Chongxuan Li

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54 papers

2 author rows

ICML Conference 2025 Conference Paper

A Theory for Conditional Generative Modeling on Multiple Data Sources

Rongzhen Wang
Yan Zhang
Chenyu Zheng
Chongxuan Li
Guoqiang Wu

The success of large generative models has driven a paradigm shift, leveraging massive multi-source data to enhance model capabilities. However, the interaction among these sources remains theoretically underexplored. This paper provides a first attempt to fill this gap by rigorously analyzing multi-source training in conditional generative modeling, where each condition represents a distinct data source. Specifically, we establish a general distribution estimation error bound in average total variation distance for conditional maximum likelihood estimation based on the bracketing number. Our result shows that when source distributions share certain similarities and the model is expressive enough, multi-source training guarantees a sharper bound than single-source training. We further instantiate the general theory on conditional Gaussian estimation and deep generative models including autoregressive and flexible energy-based models, by characterizing their bracketing numbers. The results highlight that the number of sources and similarity among source distributions improve the advantage of multi-source training. Simulations and real-world experiments validate our theory.

ICML Conference 2025 Conference Paper

Effective and Efficient Masked Image Generation Models

Zebin You
Jingyang Ou
Xiaolu Zhang
Jun Hu
Jun Zhou 0011
Chongxuan Li

Although masked image generation models and masked diffusion models are designed with different motivations and objectives, we observe that they can be unified within a single framework. Building upon this insight, we carefully explore the design space of training and sampling, identifying key factors that contribute to both performance and efficiency. Based on the improvements observed during this exploration, we develop our model, referred to as eMIGM. Empirically, eMIGM demonstrates strong performance on ImageNet generation, as measured by Fréchet Inception Distance (FID). In particular, on ImageNet $256\times256$, with similar number of function evaluations (NFEs) and model parameters, eMIGM outperforms the seminal VAR. Moreover, as NFE and model parameters increase, eMIGM achieves performance comparable to the state-of-the-art continuous diffusion model REPA while requiring less than 45% of the NFE. Additionally, on ImageNet $512\times512$, eMIGM outperforms the strong continuous diffusion model EDM2. Code is available at https: //github. com/ML-GSAI/eMIGM.

NeurIPS Conference 2025 Conference Paper

FlexWorld: Progressively Expanding 3D Scenes for Flexible-View Exploration

Luxi Chen
Zihan Zhou
Min Zhao
Yikai Wang
Ge Zhang
Wenhao Huang
Hao Sun
Ji-Rong Wen

Generating flexible-view 3D scenes, including 360° rotation and zooming, from single images is challenging due to a lack of 3D data. To this end, we introduce FlexWorld, a novel framework that progressively constructs a persistent 3D Gaussian splatting representation by synthesizing and integrating new 3D content. To handle novel view synthesis under large camera variations, we leverage an advanced pre-trained video model fine-tuned on accurate depth-estimated training pairs. By combining geometry-aware scene integration and optimization, FlexWorld refines the scene representation, producing visually consistent 3D scenes with flexible viewpoints. Extensive experiments demonstrate the effectiveness of FlexWorld in generating high-quality novel view videos and flexible-view 3D scenes from single images, achieving superior visual quality under multiple popular metrics and datasets compared to existing state-of-the-art methods. Additionally, FlexWorld supports extrapolating from existing 3D scenes, further extending its applicability. Qualitatively, we highlight that FlexWorld can generate high-fidelity scenes that enable 360° rotations and zooming exploration. Our code is available at https: //github. com/ML-GSAI/FlexWorld.

ICLR Conference 2025 Conference Paper

Improving Long-Text Alignment for Text-to-Image Diffusion Models

Luping Liu
Chao Du
Tianyu Pang
Zehan Wang 0001
Chongxuan Li
Dong Xu

The rapid advancement of text-to-image (T2I) diffusion models has enabled them to generate unprecedented results from given texts. However, as text inputs become longer, existing encoding methods like CLIP face limitations, and aligning the generated images with long texts becomes challenging. To tackle these issues, we propose LongAlign, which includes a segment-level encoding method for processing long texts and a decomposed preference optimization method for effective alignment training. For segment-level encoding, long texts are divided into multiple segments and processed separately. This method overcomes the maximum input length limits of pretrained encoding models. For preference optimization, we provide decomposed CLIP-based preference models to fine-tune diffusion models. Specifically, to utilize CLIP-based preference models for T2I alignment, we delve into their scoring mechanisms and find that the preference scores can be decomposed into two components: a text-relevant part that measures T2I alignment and a text-irrelevant part that assesses other visual aspects of human preference. Additionally, we find that the text-irrelevant part contributes to a common overfitting problem during fine-tuning. To address this, we propose a reweighting strategy that assigns different weights to these two components, thereby reducing overfitting and enhancing alignment. After fine-tuning $512 \\times 512$ Stable Diffusion (SD) v1.5 for about 20 hours using our method, the fine-tuned SD outperforms stronger foundation models in T2I alignment, such as PixArt-$\\alpha$ and Kandinsky v2.2. The code is available at https://github.com/luping-liu/LongAlign.

NeurIPS Conference 2025 Conference Paper

Large Language Diffusion Models

Shen Nie
Fengqi Zhu
Zebin You
Xiaolu Zhang
Jingyang Ou
Jun Hu
Jun Zhou
Yankai Lin

The capabilities of large language models (LLMs) are widely regarded as relying on autoregressive models (ARMs). We challenge this notion by introducing LLaDA, a diffusion model trained from scratch under the pre-training and supervised fine-tuning (SFT) paradigm. LLaDA employs a forward data masking process and a reverse generation process, parameterized by a Transformer to predict masked tokens. It provides a principled generative approach for probabilistic inference by optimizing a likelihood lower bound. Across extensive benchmarks on general tasks, math, code, and so on, LLaDA demonstrates strong scalability and performs comparably to our self-constructed ARM baselines. Remarkably, LLaDA 8B is competitive with strong LLMs like LLaMA3 8B in in-context learning and, after SFT, exhibits impressive instruction-following abilities in case studies such as multi-turn dialogue. Moreover, LLaDA addresses the reversal curse, surpassing GPT-4o in a reversal poem completion task. Our findings show the promise of diffusion models for language modeling at scale and challenge the common assumption that core LLM capabilities discussed above inherently depend on ARMs. Project page and codes: \url{https: //ml-gsai. github. io/LLaDA-demo/}.

NeurIPS Conference 2025 Conference Paper

Masked Diffusion Models as Energy Minimization

Sitong Chen
Shen Nie
Jiacheng Sun
Zijin Feng
Zhenguo Li
Ji-Rong Wen
Chongxuan Li

We present a systematic theoretical framework that interprets masked diffusion models (MDMs) as solutions to energy minimization problems in discrete optimal transport. Specifically, we prove that three distinct energy formulations—kinetic, conditional kinetic, and geodesic energy—are mathematically equivalent under the structure of MDMs, and that MDMs minimize all three when the mask schedule satisfies a closed-form optimality condition. This unification not only clarifies the theoretical foundations of MDMs, but also motivates practical improvements in sampling. By parameterizing interpolation schedules via Beta distributions, we reduce the schedule design space to a tractable 2D search, enabling efficient post-training tuning without model modification. Experiments on synthetic and real-world benchmarks demonstrate that our energy-inspired schedules outperform hand-crafted baselines, particularly in low-step sampling settings.

TMLR Journal 2025 Journal Article

On Memorization in Diffusion Models

Xiangming Gu
Chao Du
Tianyu Pang
Chongxuan Li
Min Lin
Ye Wang

Due to their capacity to generate novel and high-quality samples, diffusion models have attracted significant research interest in recent years. Notably, the typical training objective of diffusion models, i.e., denoising score matching, has a closed-form optimal solution that can only generate training-data replicating samples. This indicates that a memorization behavior is theoretically expected, which contradicts the common generalization ability of state-of-the-art diffusion models, and thus calls for a deeper understanding. Looking into this, we first observe that memorization behaviors tend to occur on smaller-sized datasets, which motivates our definition of effective model memorization (EMM), a metric measuring the maximum size of training data at which a model approximates its theoretical optimum. Then, we quantify the impact of the influential factors on these memorization behaviors in terms of EMM, focusing primarily on data distribution, model configuration, and training procedure. Besides comprehensive empirical results identifying the influential factors, we surprisingly find that conditioning training data on uninformative random labels can significantly trigger the memorization in diffusion models. Our study holds practical significance for diffusion model users and offers clues to theoretical research in deep generative models.

ICML Conference 2025 Conference Paper

RIFLEx: A Free Lunch for Length Extrapolation in Video Diffusion Transformers

Min Zhao 0013
Guande He
Yixiao Chen
Hongzhou Zhu
Chongxuan Li
Jun Zhu 0001

Recent advancements in video generation have enabled models to synthesize high-quality, minute-long videos. However, generating even longer videos with temporal coherence remains a major challenge and existing length extrapolation methods lead to temporal repetition or motion deceleration. In this work, we systematically analyze the role of frequency components in positional embeddings and identify an intrinsic frequency that primarily governs extrapolation behavior. Based on this insight, we propose RIFLEx, a minimal yet effective approach that reduces the intrinsic frequency to suppress repetition while preserving motion consistency, without requiring any additional modifications. RIFLEx offers a true free lunch—achieving high-quality $2\times$ extrapolation on state-of-the-art video diffusion transformers in a completely training-free manner. Moreover, it enhances quality and enables $3\times$ extrapolation by minimal fine-tuning without long videos.

NeurIPS Conference 2025 Conference Paper

Scaling Diffusion Transformers Efficiently via $\mu$P

Chenyu Zheng
Xinyu Zhang
Rongzhen Wang
Wei Huang
Zhi Tian
Weilin Huang
Jun Zhu
Chongxuan Li

Diffusion Transformers have emerged as the foundation for vision generative models, but their scalability is limited by the high cost of hyperparameter (HP) tuning at large scales. Recently, Maximal Update Parametrization ($\mu$P) was proposed for vanilla Transformers, which enables stable HP transfer from small to large language models, and dramatically reduces tuning costs. However, it remains unclear whether $\mu$P of vanilla Transformers extends to diffusion Transformers, which differ architecturally and objectively. In this work, we generalize $\mu$P to diffusion Transformers and validate its effectiveness through large-scale experiments. First, we rigorously prove that $\mu$P of mainstream diffusion Transformers, including DiT, U-ViT, PixArt-$\alpha$, and MMDiT, aligns with that of the vanilla Transformer, enabling the direct application of existing $\mu$P methodologies. Leveraging this result, we systematically demonstrate that DiT-$\mu$P enjoys robust HP transferability. Notably, DiT-XL-2-$\mu$P with transferred learning rate achieves 2. 9$\times$ faster convergence than the original DiT-XL-2. Finally, we validate the effectiveness of $\mu$P on text-to-image generation by scaling PixArt-$\alpha$ from 0. 04B to 0. 61B and MMDiT from 0. 18B to 18B. In both cases, models under $\mu$P outperform their respective baselines while requiring small tuning cost—only 5. 5% of one training run for PixArt-$\alpha$ and 3% of consumption by human experts for MMDiT-18B. \textit{These results establish $\mu$P as a principled and efficient framework for scaling diffusion Transformers}.

ICLR Conference 2025 Conference Paper

Scaling up Masked Diffusion Models on Text

Shen Nie
Fengqi Zhu
Chao Du
Tianyu Pang
Qian Liu 0033
Guangtao Zeng
Min Lin
Chongxuan Li

Masked diffusion models (MDMs) have shown promise in language modeling, yet their scalability and effectiveness in core language tasks, such as text generation and language understanding, remain underexplored. This paper establishes the first scaling law for MDMs, demonstrating a scaling rate comparable to autoregressive models (ARMs) and a relatively small compute gap. Motivated by their scalability, we train a family of MDMs with up to 1.1 billion (B) parameters to systematically evaluate their performance against ARMs of comparable or larger sizes. Fully leveraging the probabilistic formulation of MDMs, we propose a simple yet effective *unsupervised classifier-free guidance* that effectively exploits large-scale unpaired data, boosting performance for conditional inference. In language understanding, the 1.1B MDM outperforms the 1.1B TinyLlama model trained on the same data across four of eight zero-shot benchmarks. Notably, it achieves competitive math reasoning ability with the 7B Llama-2 model on the GSM8K dataset. In text generation, MDMs with 16 times more pre-training time offer a flexible trade-off against ARMs with the accelerated sampling technique KV-Cache: MDMs match ARMs in performance while being 1.4 times faster during sampling. Moreover, MDMs address challenging tasks for ARMs by effectively handling bidirectional reasoning and adapting to temporal shifts in data. Notably, a 1.1B MDM breaks the *reverse curse* encountered by much larger ARMs with significantly more data and computation, such as 13B Llama-2 and 175B GPT-3. Our code is available at https://github.com/ML-GSAI/SMDM.

ICLR Conference 2025 Conference Paper

Your Absorbing Discrete Diffusion Secretly Models the Conditional Distributions of Clean Data

Jingyang Ou
Shen Nie
Kaiwen Xue
Fengqi Zhu
Jiacheng Sun
Zhenguo Li
Chongxuan Li

Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete score. In this paper, we reveal that the concrete score in absorbing diffusion can be expressed as conditional probabilities of clean data, multiplied by a time-dependent scalar in an analytic form. Motivated by this finding, we propose reparameterized absorbing discrete diffusion (RADD), a dedicated diffusion model without time-condition that characterizes the time-independent conditional probabilities. Besides its simplicity, RADD can reduce the number of function evaluations (NFEs) by caching the output of the time-independent network when the noisy sample remains unchanged in a sampling interval, which enables sampling acceleration. Built upon the new perspective of conditional distributions, we further unify absorbing discrete diffusion and any-order autoregressive models (AO-ARMs), showing that the upper bound on the negative log-likelihood for the diffusion model can be interpreted as an expected negative log-likelihood for AO-ARMs. Further, our RADD models achieve SOTA performance among diffusion models on 5 zero-shot language modeling benchmarks (measured by perplexity) at the GPT-2 scale. Our code is available at \url{https://github.com/ML-GSAI/RADD}.

ICLR Conference 2024 Conference Paper

BayesDiff: Estimating Pixel-wise Uncertainty in Diffusion via Bayesian Inference

Siqi Kou
Lei Gan
Dequan Wang
Chongxuan Li
Zhijie Deng

Diffusion models have impressive image generation capability, but low-quality generations still exist, and their identification remains challenging due to the lack of a proper sample-wise metric. To address this, we propose BayesDiff, a pixel-wise uncertainty estimator for generations from diffusion models based on Bayesian inference. In particular, we derive a novel uncertainty iteration principle to characterize the uncertainty dynamics in diffusion, and leverage the last-layer Laplace approximation for efficient Bayesian inference. The estimated pixel-wise uncertainty can not only be aggregated into a sample-wise metric to filter out low-fidelity images but also aids in augmenting successful generations and rectifying artifacts in failed generations in text-to-image tasks. Extensive experiments demonstrate the efficacy of BayesDiff and its promise for practical applications.

ICML Conference 2024 Conference Paper

EquiPocket: an E(3)-Equivariant Geometric Graph Neural Network for Ligand Binding Site Prediction

Yang Zhang 0094
Zhewei Wei
Ye Yuan 0001
Chongxuan Li
Wenbing Huang 0001

Predicting the binding sites of target proteins plays a fundamental role in drug discovery. Most existing deep-learning methods consider a protein as a 3D image by spatially clustering its atoms into voxels and then feed the voxelized protein into a 3D CNN for prediction. However, the CNN-based methods encounter several critical issues: 1) defective in representing irregular protein structures; 2) sensitive to rotations; 3) insufficient to characterize the protein surface; 4) unaware of protein size shift. To address the above issues, this work proposes EquiPocket, an E(3)-equivariant Graph Neural Network (GNN) for binding site prediction, which comprises three modules: the first one to extract local geometric information for each surface atom, the second one to model both the chemical and spatial structure of protein and the last one to capture the geometry of the surface via equivariant message passing over the surface atoms. We further propose a dense attention output layer to alleviate the effect incurred by variable protein size. Extensive experiments on several representative benchmarks demonstrate the superiority of our framework to the state-of-the-art methods.

NeurIPS Conference 2024 Conference Paper

Graph Diffusion Policy Optimization

Yijing Liu
Chao Du
Tianyu Pang
Chongxuan Li
Min Lin
Wei Chen

Recent research has made significant progress in optimizing diffusion models for downstream objectives, which is an important pursuit in fields such as graph generation for drug design. However, directly applying these models to graph presents challenges, resulting in suboptimal performance. This paper introduces graph diffusion policy optimization (GDPO), a novel approach to optimize graph diffusion models for arbitrary (e. g. , non-differentiable) objectives using reinforcement learning. GDPO is based on an eager policy gradient tailored for graph diffusion models, developed through meticulous analysis and promising improved performance. Experimental results show that GDPO achieves state-of-the-art performance in various graph generation tasks with complex and diverse objectives. Code is available at https: //github. com/sail-sg/GDPO.

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NeurIPS Conference 2024 Conference Paper

Identifying and Solving Conditional Image Leakage in Image-to-Video Diffusion Model

Min Zhao
Hongzhou Zhu
Chendong Xiang
Kaiwen Zheng
Chongxuan Li
Jun Zhu

Diffusion models have obtained substantial progress in image-to-video generation. However, in this paper, we find that these models tend to generate videos with less motion than expected. We attribute this to the issue called conditional image leakage, where the image-to-video diffusion models (I2V-DMs) tend to over-rely on the conditional image at large time steps. We further address this challenge from both inference and training aspects. First, we propose to start the generation process from an earlier time step to avoid the unreliable large-time steps of I2V-DMs, as well as an initial noise distribution with optimal analytic expressions (Analytic-Init) by minimizing the KL divergence between it and the actual marginal distribution to bridge the training-inference gap. Second, we design a time-dependent noise distribution (TimeNoise) for the conditional image during training, applying higher noise levels at larger time steps to disrupt it and reduce the model's dependency on it. We validate these general strategies on various I2V-DMs on our collected open-domain image benchmark and the UCF101 dataset. Extensive results show that our methods outperform baselines by producing higher motion scores with lower errors while maintaining image alignment and temporal consistency, thereby yielding superior overall performance and enabling more accurate motion control. The project page: \url{https: //cond-image-leak. github. io/}.

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NeurIPS Conference 2024 Conference Paper

Lower Bounds of Uniform Stability in Gradient-Based Bilevel Algorithms for Hyperparameter Optimization

Rongzhen Wang
Chenyu Zheng
Guoqiang Wu
Xu Min
Xiaolu Zhang
Jun Zhou
Chongxuan Li

Gradient-based bilevel programming leverages unrolling differentiation (UD) or implicit function theorem (IFT) to solve hyperparameter optimization (HO) problems, and is proven effective and scalable in practice. To understand their generalization behavior, existing works establish upper bounds on the uniform stability of these algorithms, while their tightness is still unclear. To this end, this paper attempts to establish stability lower bounds for UD-based and IFT-based algorithms. A central technical challenge arises from the dependency of each outer-level update on the concurrent stage of inner optimization in bilevel programming. To address this problem, we introduce lower-bounded expansion properties to characterize the instability in update rules which can serve as general tools for lower-bound analysis. These properties guarantee the hyperparameter divergence at the outer level and the Lipschitz constant of inner output at the inner level in the context of HO. Guided by these insights, we construct a quadratic example that yields tight lower bounds for the UD-based algorithm and meaningful bounds for a representative IFT-based algorithm. Our tight result indicates that uniform stability has reached its limit in stability analysis for the UD-based algorithm.

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NeurIPS Conference 2024 Conference Paper

On Mesa-Optimization in Autoregressively Trained Transformers: Emergence and Capability

Chenyu Zheng
Wei Huang
Rongzhen Wang
Guoqiang Wu
Jun Zhu
Chongxuan Li

Autoregressively trained transformers have brought a profound revolution to the world, especially with their in-context learning (ICL) ability to address downstream tasks. Recently, several studies suggest that transformers learn a mesa-optimizer during autoregressive (AR) pretraining to implement ICL. Namely, the forward pass of the trained transformer is equivalent to optimizing an inner objective function in-context. However, whether the practical non-convex training dynamics will converge to the ideal mesa-optimizer is still unclear. Towards filling this gap, we investigate the non-convex dynamics of a one-layer linear causal self-attention model autoregressively trained by gradient flow, where the sequences are generated by an AR process $x_{t+1} = W x_t$. First, under a certain condition of data distribution, we prove that an autoregressively trained transformer learns $W$ by implementing one step of gradient descent to minimize an ordinary least squares (OLS) problem in-context. It then applies the learned $\widehat{W}$ for next-token prediction, thereby verifying the mesa-optimization hypothesis. Next, under the same data conditions, we explore the capability limitations of the obtained mesa-optimizer. We show that a stronger assumption related to the moments of data is the sufficient and necessary condition that the learned mesa-optimizer recovers the distribution. Besides, we conduct exploratory analyses beyond the first data condition and prove that generally, the trained transformer will not perform vanilla gradient descent for the OLS problem. Finally, our simulation results verify the theoretical results.

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ICLR Conference 2024 Conference Paper

The Blessing of Randomness: SDE Beats ODE in General Diffusion-based Image Editing

Shen Nie
Hanzhong Allan Guo
Cheng Lu 0011
Yuhao Zhou
Chenyu Zheng
Chongxuan Li

We present a unified probabilistic formulation for diffusion-based image editing, where a latent variable is edited in a task-specific manner and generally deviates from the corresponding marginal distribution induced by the original stochastic or ordinary differential equation (SDE or ODE). Instead, it defines a corresponding SDE or ODE for editing. In the formulation, we prove that the Kullback-Leibler divergence between the marginal distributions of the two SDEs gradually decreases while that for the ODEs remains as the time approaches zero, which shows the promise of SDE in image editing. Inspired by it, we provide the SDE counterparts for widely used ODE baselines in various tasks including inpainting and image-to-image translation, where SDE shows a consistent and substantial improvement. Moreover, we propose \emph{SDE-Drag} -- a simple yet effective method built upon the SDE formulation for point-based content dragging. We build a challenging benchmark (termed \emph{DragBench}) with open-set natural, art, and AI-generated images for evaluation. A user study on DragBench indicates that SDE-Drag significantly outperforms our ODE baseline, existing diffusion-based methods, and the renowned DragGAN. Our results demonstrate the superiority and versatility of SDE in image editing and push the boundary of diffusion-based editing methods. See the project page \url{https://ml-gsai.github.io/SDE-Drag-demo/} for the code and DragBench dataset.

ICML Conference 2024 Conference Paper

Unifying Bayesian Flow Networks and Diffusion Models through Stochastic Differential Equations

Kaiwen Xue
Yuhao Zhou
Shen Nie
Xu Min
Xiaolu Zhang
Jun Zhou 0011
Chongxuan Li

Bayesian flow networks (BFNs) iteratively refine the parameters, instead of the samples in diffusion models (DMs), of distributions at various noise levels through Bayesian inference. Owing to its differentiable nature, BFNs are promising in modeling both continuous and discrete data, while simultaneously maintaining fast sampling capabilities. This paper aims to understand and enhance BFNs by connecting them with DMs through stochastic differential equations (SDEs). We identify the linear SDEs corresponding to the noise-addition processes in BFNs, demonstrate that BFN’s regression losses are aligned with denoise score matching, and validate the sampler in BFN as a first-order solver for the respective reverse-time SDE. Based on these findings and existing recipes of fast sampling in DMs, we propose specialized solvers for BFNs that markedly surpass the original BFN sampler in terms of sample quality with a limited number of function evaluations (e. g. , 10) on both image and text datasets. Notably, our best sampler achieves an increase in speed of $5\sim20$ times for free.

ICML Conference 2023 Conference Paper

Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning

Cheng Lu 0011
Huayu Chen
Jianfei Chen 0001
Hang Su 0006
Chongxuan Li
Jun Zhu 0001

Guided sampling is a vital approach for applying diffusion models in real-world tasks that embeds human-defined guidance during the sampling procedure. This paper considers a general setting where the guidance is defined by an (unnormalized) energy function. The main challenge for this setting is that the intermediate guidance during the diffusion sampling procedure, which is jointly defined by the sampling distribution and the energy function, is unknown and is hard to estimate. To address this challenge, we propose an exact formulation of the intermediate guidance as well as a novel training objective named contrastive energy prediction (CEP) to learn the exact guidance. Our method is guaranteed to converge to the exact guidance under unlimited model capacity and data samples, while previous methods can not. We demonstrate the effectiveness of our method by applying it to offline reinforcement learning (RL). Extensive experiments on D4RL benchmarks demonstrate that our method outperforms existing state-of-the-art algorithms. We also provide some examples of applying CEP for image synthesis to demonstrate the scalability of CEP on high-dimensional data.

ICLR Conference 2023 Conference Paper

Deep Generative Modeling on Limited Data with Regularization by Nontransferable Pre-trained Models

Yong Zhong
Hongtao Liu
Xiaodong Liu
Fan Bao
Weiran Shen
Chongxuan Li

Deep generative models (DGMs) are data-eager because learning a complex model on limited data suffers from a large variance and easily overfits. Inspired by the classical perspective of the bias-variance tradeoff, we propose regularized deep generative model (Reg-DGM), which leverages a nontransferable pre-trained model to reduce the variance of generative modeling with limited data. Formally, Reg-DGM optimizes a weighted sum of a certain divergence and the expectation of an energy function, where the divergence is between the data and the model distributions, and the energy function is defined by the pre-trained model w.r.t. the model distribution. We analyze a simple yet representative Gaussian-fitting case to demonstrate how the weighting hyperparameter trades off the bias and the variance. Theoretically, we characterize the existence and the uniqueness of the global minimum of Reg-DGM in a non-parametric setting and prove its convergence with neural networks trained by gradient-based methods. Empirically, with various pre-trained feature extractors and a data-dependent energy function, Reg-DGM consistently improves the generation performance of strong DGMs with limited data and achieves competitive results to the state-of-the-art methods. Our implementation is available at https://github.com/ML-GSAI/Reg-ADA-APA.

NeurIPS Conference 2023 Conference Paper

Diffusion Models and Semi-Supervised Learners Benefit Mutually with Few Labels

Zebin You
Yong Zhong
Fan Bao
Jiacheng Sun
Chongxuan Li
Jun Zhu

In an effort to further advance semi-supervised generative and classification tasks, we propose a simple yet effective training strategy called *dual pseudo training* (DPT), built upon strong semi-supervised learners and diffusion models. DPT operates in three stages: training a classifier on partially labeled data to predict pseudo-labels; training a conditional generative model using these pseudo-labels to generate pseudo images; and retraining the classifier with a mix of real and pseudo images. Empirically, DPT consistently achieves SOTA performance of semi-supervised generation and classification across various settings. In particular, with one or two labels per class, DPT achieves a Fréchet Inception Distance (FID) score of 3. 08 or 2. 52 on ImageNet $256\times256$. Besides, DPT outperforms competitive semi-supervised baselines substantially on ImageNet classification tasks, *achieving top-1 accuracies of 59. 0 (+2. 8), 69. 5 (+3. 0), and 74. 4 (+2. 0)* with one, two, or five labels per class, respectively. Notably, our results demonstrate that diffusion can generate realistic images with only a few labels (e. g. , $<0. 1$%) and generative augmentation remains viable for semi-supervised classification. Our code is available at *https: //github. com/ML-GSAI/DPT*.

ICLR Conference 2023 Conference Paper

Equivariant Energy-Guided SDE for Inverse Molecular Design

Fan Bao
Min Zhao 0013
Zhongkai Hao
Peiyao Li
Chongxuan Li
Jun Zhu 0001

Inverse molecular design is critical in material science and drug discovery, where the generated molecules should satisfy certain desirable properties. In this paper, we propose equivariant energy-guided stochastic differential equations (EEGSDE), a flexible framework for controllable 3D molecule generation under the guidance of an energy function in diffusion models. Formally, we show that EEGSDE naturally exploits the geometric symmetry in 3D molecular conformation, as long as the energy function is invariant to orthogonal transformations. Empirically, under the guidance of designed energy functions, EEGSDE significantly improves the baseline on QM9, in inverse molecular design targeted to quantum properties and molecular structures. Furthermore, EEGSDE is able to generate molecules with multiple target properties by combining the corresponding energy functions linearly.

NeurIPS Conference 2023 Conference Paper

Gaussian Mixture Solvers for Diffusion Models

Hanzhong Guo
Cheng Lu
Fan Bao
Tianyu Pang
Shuicheng Yan
Chao Du
Chongxuan Li

Recently, diffusion models have achieved great success in generative tasks. Sampling from diffusion models is equivalent to solving the reverse diffusion stochastic differential equations (SDEs) or the corresponding probability flow ordinary differential equations (ODEs). In comparison, SDE-based solvers can generate samples of higher quality and are suited for image translation tasks like stroke-based synthesis. During inference, however, existing SDE-based solvers are severely constrained by the efficiency-effectiveness dilemma. Our investigation suggests that this is because the Gaussian assumption in the reverse transition kernel is frequently violated (even in the case of simple mixture data) given a limited number of discretization steps. To overcome this limitation, we introduce a novel class of SDE-based solvers called \emph{Gaussian Mixture Solvers (GMS)} for diffusion models. Our solver estimates the first three-order moments and optimizes the parameters of a Gaussian mixture transition kernel using generalized methods of moments in each step during sampling. Empirically, our solver outperforms numerous SDE-based solvers in terms of sample quality in image generation and stroke-based synthesis in various diffusion models, which validates the motivation and effectiveness of GMS. Our code is available at https: //github. com/Guohanzhong/GMS.

NeurIPS Conference 2023 Conference Paper

On Evaluating Adversarial Robustness of Large Vision-Language Models

Yunqing Zhao
Tianyu Pang
Chao Du
Xiao Yang
Chongxuan Li
Ngai-Man (Man) Cheung
Min Lin

Large vision-language models (VLMs) such as GPT-4 have achieved unprecedented performance in response generation, especially with visual inputs, enabling more creative and adaptable interaction than large language models such as ChatGPT. Nonetheless, multimodal generation exacerbates safety concerns, since adversaries may successfully evade the entire system by subtly manipulating the most vulnerable modality (e. g. , vision). To this end, we propose evaluating the robustness of open-source large VLMs in the most realistic and high-risk setting, where adversaries have only black-box system access and seek to deceive the model into returning the targeted responses. In particular, we first craft targeted adversarial examples against pretrained models such as CLIP and BLIP, and then transfer these adversarial examples to other VLMs such as MiniGPT-4, LLaVA, UniDiffuser, BLIP-2, and Img2Prompt. In addition, we observe that black-box queries on these VLMs can further improve the effectiveness of targeted evasion, resulting in a surprisingly high success rate for generating targeted responses. Our findings provide a quantitative understanding regarding the adversarial vulnerability of large VLMs and call for a more thorough examination of their potential security flaws before deployment in practice. Our project page: https: //yunqing-me. github. io/AttackVLM/.

ICML Conference 2023 Conference Paper

One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale

Fan Bao
Shen Nie
Kaiwen Xue
Chongxuan Li
Shi Pu 0002
Yaole Wang
Gang Yue
Yue Cao

This paper proposes a unified diffusion framework (dubbed UniDiffuser) to fit all distributions relevant to a set of multi-modal data in one model. Our key insight is – learning diffusion models for marginal, conditional, and joint distributions can be unified as predicting the noise in the perturbed data, where the perturbation levels (i. e. timesteps) can be different for different modalities. Inspired by the unified view, UniDiffuser learns all distributions simultaneously with a minimal modification to the original diffusion model – perturbs data in all modalities instead of a single modality, inputs individual timesteps in different modalities, and predicts the noise of all modalities instead of a single modality. UniDiffuser is parameterized by a transformer for diffusion models to handle input types of different modalities. Implemented on large-scale paired image-text data, UniDiffuser is able to perform image, text, text-to-image, image-to-text, and image-text pair generation by setting proper timesteps without additional overhead. In particular, UniDiffuser is able to produce perceptually realistic samples in all tasks and its quantitative results (e. g. , the FID and CLIP score) are not only superior to existing general-purpose models but also comparable to the bespoken models (e. g. , Stable Diffusion and DALL-E 2) in representative tasks (e. g. , text-to-image generation).

NeurIPS Conference 2023 Conference Paper

ProlificDreamer: High-Fidelity and Diverse Text-to-3D Generation with Variational Score Distillation

Zhengyi Wang
Cheng Lu
Yikai Wang
Fan Bao
Chongxuan Li
Hang Su
Jun Zhu

Score distillation sampling (SDS) has shown great promise in text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models, but suffers from over-saturation, over-smoothing, and low-diversity problems. In this work, we propose to model the 3D parameter as a random variable instead of a constant as in SDS and present *variational score distillation* (VSD), a principled particle-based variational framework to explain and address the aforementioned issues in text-to-3D generation. We show that SDS is a special case of VSD and leads to poor samples with both small and large CFG weights. In comparison, VSD works well with various CFG weights as ancestral sampling from diffusion models and simultaneously improves the diversity and sample quality with a common CFG weight (i. e. , 7. 5). We further present various improvements in the design space for text-to-3D such as distillation time schedule and density initialization, which are orthogonal to the distillation algorithm yet not well explored. Our overall approach, dubbed *ProlificDreamer*, can generate high rendering resolution (i. e. , 512$\times$512) and high-fidelity NeRF with rich structure and complex effects (e. g. , smoke and drops). Further, initialized from NeRF, meshes fine-tuned by VSD are meticulously detailed and photo-realistic.

ICML Conference 2023 Conference Paper

Revisiting Discriminative vs. Generative Classifiers: Theory and Implications

Chenyu Zheng
Guoqiang Wu
Fan Bao
Yue Cao
Chongxuan Li
Jun Zhu 0001

A large-scale deep model pre-trained on massive labeled or unlabeled data transfers well to downstream tasks. Linear evaluation freezes parameters in the pre-trained model and trains a linear classifier separately, which is efficient and attractive for transfer. However, little work has investigated the classifier in linear evaluation except for the default logistic regression. Inspired by the statistical efficiency of naive Bayes, the paper revisits the classical topic on discriminative vs. generative classifiers. Theoretically, the paper considers the surrogate loss instead of the zero-one loss in analyses and generalizes the classical results from binary cases to multiclass ones. We show that, under mild assumptions, multiclass naive Bayes requires $O(\log n)$ samples to approach its asymptotic error while the corresponding multiclass logistic regression requires $O(n)$ samples, where $n$ is the feature dimension. To establish it, we present a multiclass $\mathcal{H}$-consistency bound framework and an explicit bound for logistic loss, which are of independent interests. Simulation results on a mixture of Gaussian validate our theoretical findings. Experiments on various pre-trained deep vision models show that naive Bayes consistently converges faster as the number of data increases. Besides, naive Bayes shows promise in few-shot cases and we observe the "two regimes” phenomenon in pre-trained supervised models. Our code is available at https: //github. com/ML-GSAI/Revisiting-Dis-vs-Gen-Classifiers.

NeurIPS Conference 2023 Conference Paper

Toward Understanding Generative Data Augmentation

Chenyu Zheng
Guoqiang Wu
Chongxuan Li

Generative data augmentation, which scales datasets by obtaining fake labeled examples from a trained conditional generative model, boosts classification performance in various learning tasks including (semi-)supervised learning, few-shot learning, and adversarially robust learning. However, little work has theoretically investigated the effect of generative data augmentation. To fill this gap, we establish a general stability bound in this not independently and identicallydistributed (non-i. i. d. ) setting, where the learned distribution is dependent on the original train set and generally not the same as the true distribution. Our theoretical result includes the divergence between the learned distribution and the true distribution. It shows that generative data augmentation can enjoy a faster learning rate when the order of divergence term is $o(\max\left( \log(m)\beta_m, 1 / \sqrt{m})\right)$, where $m$ is the train set size and $\beta_m$ is the corresponding stability constant. We further specify the learning setup to the Gaussian mixture model and generative adversarial nets. We prove that in both cases, though generative data augmentation does not enjoy a faster learning rate, it can improve the learning guarantees at a constant level when the train set is small, which is significant when the awful overfitting occurs. Simulation results on the Gaussian mixture model and empirical results on generative adversarial nets support our theoretical conclusions.

ICML Conference 2023 Conference Paper

Towards Understanding Generalization of Macro-AUC in Multi-label Learning

Guoqiang Wu
Chongxuan Li
Yilong Yin

Macro-AUC is the arithmetic mean of the class-wise AUCs in multi-label learning and is commonly used in practice. However, its theoretical understanding is far lacking. Toward solving it, we characterize the generalization properties of various learning algorithms based on the corresponding surrogate losses w. r. t. Macro-AUC. We theoretically identify a critical factor of the dataset affecting the generalization bounds: the label-wise class imbalance. Our results on the imbalance-aware error bounds show that the widely-used univariate loss-based algorithm is more sensitive to the label-wise class imbalance than the proposed pairwise and reweighted loss-based ones, which probably implies its worse performance. Moreover, empirical results on various datasets corroborate our theory findings. To establish it, technically, we propose a new (and more general) McDiarmid-type concentration inequality, which may be of independent interest.

ICLR Conference 2022 Conference Paper

Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models

Fan Bao
Chongxuan Li
Jun Zhu 0001
Bo Zhang 0010

Diffusion probabilistic models (DPMs) represent a class of powerful generative models. Despite their success, the inference of DPMs is expensive since it generally needs to iterate over thousands of timesteps. A key problem in the inference is to estimate the variance in each timestep of the reverse process. In this work, we present a surprising result that both the optimal reverse variance and the corresponding optimal KL divergence of a DPM have analytic forms w.r.t. its score function. Building upon it, we propose \textit{Analytic-DPM}, a training-free inference framework that estimates the analytic forms of the variance and KL divergence using the Monte Carlo method and a pretrained score-based model. Further, to correct the potential bias caused by the score-based model, we derive both lower and upper bounds of the optimal variance and clip the estimate for a better result. Empirically, our analytic-DPM improves the log-likelihood of various DPMs, produces high-quality samples, and meanwhile enjoys a $20\times$ to $80\times$ speed up.

NeurIPS Conference 2022 Conference Paper

DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps

Cheng Lu
Yuhao Zhou
Fan Bao
Jianfei Chen
Chongxuan Li
Jun Zhu

Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works. By applying change-of-variable, the solution can be equivalently simplified to an exponentially weighted integral of the neural network. Based on our formulation, we propose DPM-Solver, a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. DPM-Solver is suitable for both discrete-time and continuous-time DPMs without any further training. Experimental results show that DPM-Solver can generate high-quality samples in only 10 to 20 function evaluations on various datasets. We achieve 4. 70 FID in 10 function evaluations and 2. 87 FID in 20 function evaluations on the CIFAR10 dataset, and a 4~16x speedup compared with previous state-of-the-art training-free samplers on various datasets.

NeurIPS Conference 2022 Conference Paper

EGSDE: Unpaired Image-to-Image Translation via Energy-Guided Stochastic Differential Equations

Min Zhao
Fan Bao
Chongxuan Li
Jun Zhu

Score-based diffusion models (SBDMs) have achieved the SOTA FID results in unpaired image-to-image translation (I2I). However, we notice that existing methods totally ignore the training data in the source domain, leading to sub-optimal solutions for unpaired I2I. To this end, we propose energy-guided stochastic differential equations (EGSDE) that employs an energy function pretrained on both the source and target domains to guide the inference process of a pretrained SDE for realistic and faithful unpaired I2I. Building upon two feature extractors, we carefully design the energy function such that it encourages the transferred image to preserve the domain-independent features and discard domain-specific ones. Further, we provide an alternative explanation of the EGSDE as a product of experts, where each of the three experts (corresponding to the SDE and two feature extractors) solely contributes to faithfulness or realism. Empirically, we compare EGSDE to a large family of baselines on three widely-adopted unpaired I2I tasks under four metrics. EGSDE not only consistently outperforms existing SBDMs-based methods in almost all settings but also achieves the SOTA realism results without harming the faithful performance. Furthermore, EGSDE allows for flexible trade-offs between realism and faithfulness and we improve the realism results further (e. g. , FID of 51. 04 in Cat $\to$ Dog and FID of 50. 43 in Wild $\to$ Dog on AFHQ) by tuning hyper-parameters. The code is available at https: //github. com/ML-GSAI/EGSDE.

ICML Conference 2022 Conference Paper

Estimating the Optimal Covariance with Imperfect Mean in Diffusion Probabilistic Models

Fan Bao
Chongxuan Li
Jiacheng Sun
Jun Zhu 0001
Bo Zhang 0010

Diffusion probabilistic models (DPMs) are a class of powerful deep generative models (DGMs). Despite their success, the iterative generation process over the full timesteps is much less efficient than other DGMs such as GANs. Thus, the generation performance on a subset of timesteps is crucial, which is greatly influenced by the covariance design in DPMs. In this work, we consider diagonal and full covariances to improve the expressive power of DPMs. We derive the optimal result for such covariances, and then correct it when the mean of DPMs is imperfect. Both the optimal and the corrected ones can be decomposed into terms of conditional expectations over functions of noise. Building upon it, we propose to estimate the optimal covariance and its correction given imperfect mean by learning these conditional expectations. Our method can be applied to DPMs with both discrete and continuous timesteps. We consider the diagonal covariance in our implementation for computational efficiency. For an efficient practical implementation, we adopt a parameter sharing scheme and a two-stage training process. Empirically, our method outperforms a wide variety of covariance design on likelihood results, and improves the sample quality especially on a small number of timesteps.

ICML Conference 2022 Conference Paper

Fast Lossless Neural Compression with Integer-Only Discrete Flows

Siyu Wang
Jianfei Chen 0001
Chongxuan Li
Jun Zhu 0001
Bo Zhang 0010

By applying entropy codecs with learned data distributions, neural compressors have significantly outperformed traditional codecs in terms of compression ratio. However, the high inference latency of neural networks hinders the deployment of neural compressors in practical applications. In this work, we propose Integer-only Discrete Flows (IODF) an efficient neural compressor with integer-only arithmetic. Our work is built upon integer discrete flows, which consists of invertible transformations between discrete random variables. We propose efficient invertible transformations with integer-only arithmetic based on 8-bit quantization. Our invertible transformation is equipped with learnable binary gates to remove redundant filters during inference. We deploy IODF with TensorRT on GPUs, achieving $10\times$ inference speedup compared to the fastest existing neural compressors, while retaining the high compression rates on ImageNet32 and ImageNet64.

ICML Conference 2022 Conference Paper

Maximum Likelihood Training for Score-based Diffusion ODEs by High Order Denoising Score Matching

Cheng Lu 0011
Kaiwen Zheng
Fan Bao
Jianfei Chen 0001
Chongxuan Li
Jun Zhu 0001

Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can be used to define an ODE (“score-based diffusion ODE”) for exact likelihood evaluation. However, the relationship between the likelihood of the ODE and the score matching objective is unclear. In this work, we prove that matching the first-order score is not sufficient to maximize the likelihood of the ODE, by showing a gap between the maximum likelihood and score matching objectives. To fill up this gap, we show that the negative likelihood of the ODE can be bounded by controlling the first, second, and third-order score matching errors; and we further present a novel high-order denoising score matching method to enable maximum likelihood training of score-based diffusion ODEs. Our algorithm guarantees that the higher-order matching error is bounded by the training error and the lower-order errors. We empirically observe that by high-order score matching, score-based diffusion ODEs achieve better likelihood on both synthetic data and CIFAR-10, while retaining the high generation quality.

ICLR Conference 2022 Conference Paper

Memory Replay with Data Compression for Continual Learning

Liyuan Wang
Xingxing Zhang 0001
Kuo Yang
Longhui Yu
Chongxuan Li
Lanqing Hong
Shifeng Zhang
Zhenguo Li

Continual learning needs to overcome catastrophic forgetting of the past. Memory replay of representative old training samples has been shown as an effective solution, and achieves the state-of-the-art (SOTA) performance. However, existing work is mainly built on a small memory buffer containing a few original data, which cannot fully characterize the old data distribution. In this work, we propose memory replay with data compression to reduce the storage cost of old training samples and thus increase their amount that can be stored in the memory buffer. Observing that the trade-off between the quality and quantity of compressed data is highly nontrivial for the efficacy of memory replay, we propose a novel method based on determinantal point processes (DPPs) to efficiently determine an appropriate compression quality for currently-arrived training samples. In this way, using a naive data compression algorithm with a properly selected quality can largely boost recent strong baselines by saving more compressed data in a limited storage space. We extensively validate this across several benchmarks of class-incremental learning and in a realistic scenario of object detection for autonomous driving.

ICLR Conference 2021 Conference Paper

Implicit Normalizing Flows

Cheng Lu 0011
Jianfei Chen 0001
Chongxuan Li
Qiuhao Wang
Jun Zhu 0001

Normalizing flows define a probability distribution by an explicit invertible transformation $\boldsymbol{\mathbf{z}}=f(\boldsymbol{\mathbf{x}})$. In this work, we present implicit normalizing flows (ImpFlows), which generalize normalizing flows by allowing the mapping to be implicitly defined by the roots of an equation $F(\boldsymbol{\mathbf{z}}, \boldsymbol{\mathbf{x}})= \boldsymbol{\mathbf{0}}$. ImpFlows build on residual flows (ResFlows) with a proper balance between expressiveness and tractability. Through theoretical analysis, we show that the function space of ImpFlow is strictly richer than that of ResFlows. Furthermore, for any ResFlow with a fixed number of blocks, there exists some function that ResFlow has a non-negligible approximation error. However, the function is exactly representable by a single-block ImpFlow. We propose a scalable algorithm to train and draw samples from ImpFlows. Empirically, we evaluate ImpFlow on several classification and density modeling tasks, and ImpFlow outperforms ResFlow with a comparable amount of parameters on all the benchmarks.

ICLR Conference 2021 Conference Paper

MiCE: Mixture of Contrastive Experts for Unsupervised Image Clustering

Tsung Wei Tsai
Chongxuan Li
Jun Zhu 0001

We present Mixture of Contrastive Experts (MiCE), a unified probabilistic clustering framework that simultaneously exploits the discriminative representations learned by contrastive learning and the semantic structures captured by a latent mixture model. Motivated by the mixture of experts, MiCE employs a gating function to partition an unlabeled dataset into subsets according to the latent semantics and multiple experts to discriminate distinct subsets of instances assigned to them in a contrastive learning manner. To solve the nontrivial inference and learning problems caused by the latent variables, we further develop a scalable variant of the Expectation-Maximization (EM) algorithm for MiCE and provide proof of the convergence. Empirically, we evaluate the clustering performance of MiCE on four widely adopted natural image datasets. MiCE achieves significantly better results than various previous methods and a strong contrastive learning baseline.

NeurIPS Conference 2021 Conference Paper

Rethinking and Reweighting the Univariate Losses for Multi-Label Ranking: Consistency and Generalization

Guoqiang Wu
Chongxuan Li
Kun Xu
Jun Zhu

The (partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical efforts on multi-label ranking mainly focus on (Fisher) consistency analyses. However, there is a gap between existing theory and practice --- some inconsistent pairwise losses can lead to promising performance, while some consistent univariate losses usually have no clear superiority in practice. To take a step towards filling up this gap, this paper presents a systematic study from two complementary perspectives of consistency and generalization error bounds of learning algorithms. We theoretically find two key factors of the distribution (or dataset) that affect the learning guarantees of algorithms: the instance-wise class imbalance and the label size $c$. Specifically, in an extremely imbalanced case, the algorithm with the consistent univariate loss has an error bound of $O(c)$, while the one with the inconsistent pairwise loss depends on $O(\sqrt{c})$ as shown in prior work. This may shed light on the superior performance of pairwise methods in practice, where real datasets are usually highly imbalanced. Moreover, we present an inconsistent reweighted univariate loss-based algorithm that enjoys an error bound of $O(\sqrt{c})$ for promising performance as well as the computational efficiency of univariate losses. Finally, experimental results confirm our theoretical findings.

NeurIPS Conference 2021 Conference Paper

Stability and Generalization of Bilevel Programming in Hyperparameter Optimization

Fan Bao
Guoqiang Wu
Chongxuan Li
Jun Zhu
Bo Zhang

The (gradient-based) bilevel programming framework is widely used in hyperparameter optimization and has achieved excellent performance empirically. Previous theoretical work mainly focuses on its optimization properties, while leaving the analysis on generalization largely open. This paper attempts to address the issue by presenting an expectation bound w. r. t. the validation set based on uniform stability. Our results can explain some mysterious behaviours of the bilevel programming in practice, for instance, overfitting to the validation set. We also present an expectation bound for the classical cross-validation algorithm. Our results suggest that gradient-based algorithms can be better than cross-validation under certain conditions in a theoretical perspective. Furthermore, we prove that regularization terms in both the outer and inner levels can relieve the overfitting problem in gradient-based algorithms. In experiments on feature learning and data reweighting for noisy labels, we corroborate our theoretical findings.

ICML Conference 2021 Conference Paper

Variational (Gradient) Estimate of the Score Function in Energy-based Latent Variable Models

Fan Bao
Kun Xu 0004
Chongxuan Li
Lanqing Hong
Jun Zhu 0001
Bo Zhang 0010

This paper presents new estimates of the score function and its gradient with respect to the model parameters in a general energy-based latent variable model (EBLVM). The score function and its gradient can be expressed as combinations of expectation and covariance terms over the (generally intractable) posterior of the latent variables. New estimates are obtained by introducing a variational posterior to approximate the true posterior in these terms. The variational posterior is trained to minimize a certain divergence (e. g. , the KL divergence) between itself and the true posterior. Theoretically, the divergence characterizes upper bounds of the bias of the estimates. In principle, our estimates can be applied to a wide range of objectives, including kernelized Stein discrepancy (KSD), score matching (SM)-based methods and exact Fisher divergence with a minimal model assumption. In particular, these estimates applied to SM-based methods outperform existing methods in learning EBLVMs on several image datasets.

NeurIPS Conference 2020 Conference Paper

Bi-level Score Matching for Learning Energy-based Latent Variable Models

Fan Bao
Chongxuan Li
Kun Xu
Hang Su
Jun Zhu
Bo Zhang

Score matching (SM) provides a compelling approach to learn energy-based models (EBMs) by avoiding the calculation of partition function. However, it remains largely open to learn energy-based latent variable models (EBLVMs), except some special cases. This paper presents a bi-level score matching (BiSM) method to learn EBLVMs with general structures by reformulating SM as a bi-level optimization problem. The higher level introduces a variational posterior of the latent variables and optimizes a modified SM objective, and the lower level optimizes the variational posterior to fit the true posterior. To solve BiSM efficiently, we develop a stochastic optimization algorithm with gradient unrolling. Theoretically, we analyze the consistency of BiSM and the convergence of the stochastic algorithm. Empirically, we show the promise of BiSM in Gaussian restricted Boltzmann machines and highly nonstructural EBLVMs parameterized by deep convolutional neural networks. BiSM is comparable to the widely adopted contrastive divergence and SM methods when they are applicable; and can learn complex EBLVMs with intractable posteriors to generate natural images.

NeurIPS Conference 2020 Conference Paper

Efficient Learning of Generative Models via Finite-Difference Score Matching

Tianyu Pang
Kun Xu
Chongxuan Li
Yang Song
Stefano Ermon
Jun Zhu

Several machine learning applications involve the optimization of higher-order derivatives (e. g. , gradients of gradients) during training, which can be expensive with respect to memory and computation even with automatic differentiation. As a typical example in generative modeling, score matching~(SM) involves the optimization of the trace of a Hessian. To improve computing efficiency, we rewrite the SM objective and its variants in terms of directional derivatives, and present a generic strategy to efficiently approximate any-order directional derivative with finite difference~(FD). Our approximation only involves function evaluations, which can be executed in parallel, and no gradient computations. Thus, it reduces the total computational cost while also improving numerical stability. We provide two instantiations by reformulating variants of SM objectives into the FD forms. Empirically, we demonstrate that our methods produce results comparable to the gradient-based counterparts while being much more computationally efficient.

ICLR Conference 2020 Conference Paper

To Relieve Your Headache of Training an MRF, Take AdVIL

Chongxuan Li
Chao Du
Kun Xu 0004
Max Welling
Jun Zhu 0001
Bo Zhang 0010

We propose a black-box algorithm called {\it Adversarial Variational Inference and Learning} (AdVIL) to perform inference and learning on a general Markov random field (MRF). AdVIL employs two variational distributions to approximately infer the latent variables and estimate the partition function of an MRF, respectively. The two variational distributions provide an estimate of the negative log-likelihood of the MRF as a minimax optimization problem, which is solved by stochastic gradient descent. AdVIL is proven convergent under certain conditions. On one hand, compared with contrastive divergence, AdVIL requires a minimal assumption about the model structure and can deal with a broader family of MRFs. On the other hand, compared with existing black-box methods, AdVIL provides a tighter estimate of the log partition function and achieves much better empirical results.

ICML Conference 2020 Conference Paper

Understanding and Stabilizing GANs' Training Dynamics Using Control Theory

Kun Xu 0004
Chongxuan Li
Jun Zhu 0001
Bo Zhang 0010

Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present a conceptually novel perspective from control theory to directly model the dynamics of GANs in the frequency domain and provide simple yet effective methods to stabilize GAN’s training. We first analyze the training dynamic of a prototypical Dirac GAN and adopt the widely-used closed-loop control (CLC) to improve its stability. We then extend CLC to stabilize the training dynamic of normal GANs, which can be implemented as an L2 regularizer on the output of the discriminator. Empirical results show that our method can effectively stabilize the training and obtain state-of-the-art performance on data generation tasks.

NeurIPS Conference 2019 Conference Paper

Multi-objects Generation with Amortized Structural Regularization

Taufik Xu
Chongxuan Li
Jun Zhu
Bo Zhang

Deep generative models (DGMs) have shown promise in image generation. However, most of the existing methods learn a model by simply optimizing a divergence between the marginal distributions of the model and the data, and often fail to capture rich structures, such as attributes of objects and their relationships, in an image. Human knowledge is a crucial element to the success of DGMs to infer these structures, especially in unsupervised learning. In this paper, we propose amortized structural regularization (ASR), which adopts posterior regularization (PR) to embed human knowledge into DGMs via a set of structural constraints. We derive a lower bound of the regularized log-likelihood in PR and adopt the amortized inference technique to jointly optimize the generative model and an auxiliary recognition model for inference efficiently. Empirical results show that ASR outperforms the DGM baselines in terms of inference performance and sample quality.

AAAI Conference 2018 Conference Paper

Collaborative Filtering With User-Item Co-Autoregressive Models

Chao Du
Chongxuan Li
Yin Zheng
Jun Zhu
Bo Zhang

Deep neural networks have shown promise in collaborative ﬁltering (CF). However, existing neural approaches are either user-based or item-based, which cannot leverage all the underlying information explicitly. We propose CF-UIcA, a neural co-autoregressive model for CF tasks, which exploits the structural correlation in the domains of both users and items. The co-autoregression allows extra desired properties to be incorporated for different tasks. Furthermore, we develop an efﬁcient stochastic learning algorithm to handle large scale datasets. We evaluate CF-UIcA on two popular benchmarks: MovieLens 1M and Netﬂix, and achieve state-of-the-art performance in both rating prediction and top-N recommendation tasks, which demonstrates the effectiveness of CF-UIcA.

NeurIPS Conference 2018 Conference Paper

Graphical Generative Adversarial Networks

Chongxuan Li
Max Welling
Jun Zhu
Bo Zhang

We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data. Graphical-GAN conjoins the power of Bayesian networks on compactly representing the dependency structures among random variables and that of generative adversarial networks on learning expressive dependency functions. We introduce a structured recognition model to infer the posterior distribution of latent variables given observations. We generalize the Expectation Propagation (EP) algorithm to learn the generative model and recognition model jointly. Finally, we present two important instances of Graphical-GAN, i. e. Gaussian Mixture GAN (GMGAN) and State Space GAN (SSGAN), which can successfully learn the discrete and temporal structures on visual datasets, respectively.

IJCAI Conference 2018 Conference Paper

Learning to Write Stylized Chinese Characters by Reading a Handful of Examples

Danyang Sun
Tongzheng Ren
Chongxuan Li
Hang Su
Jun Zhu

Automatically writing stylized characters is an attractive yet challenging task, especially for Chinese characters with complex shapes and structures. Most current methods are restricted to generate stylized characters already present in the training set, but required to retrain the model when generating characters of new styles. In this paper, we develop a novel framework of Style-Aware Variational Auto-Encoder (SA-VAE), which disentangles the content-relevant and style-relevant components of a Chinese character feature with a novel intercross pair-wise optimization method. In this case, our method can generate Chinese characters flexibly by reading a few examples. Experiments demonstrate that our method has a powerful one-shot/few-shot generalization ability by inferring the style representation, which is the first attempt to learn to write new-style Chinese characters by observing only one or a few examples.

NeurIPS Conference 2017 Conference Paper

Population Matching Discrepancy and Applications in Deep Learning

Jianfei Chen
Chongxuan Li
Yizhong Ru
Jun Zhu

A differentiable estimation of the distance between two distributions based on samples is important for many deep learning tasks. One such estimation is maximum mean discrepancy (MMD). However, MMD suffers from its sensitive kernel bandwidth hyper-parameter, weak gradients, and large mini-batch size when used as a training objective. In this paper, we propose population matching discrepancy (PMD) for estimating the distribution distance based on samples, as well as an algorithm to learn the parameters of the distributions using PMD as an objective. PMD is defined as the minimum weight matching of sample populations from each distribution, and we prove that PMD is a strongly consistent estimator of the first Wasserstein metric. We apply PMD to two deep learning tasks, domain adaptation and generative modeling. Empirical results demonstrate that PMD overcomes the aforementioned drawbacks of MMD, and outperforms MMD on both tasks in terms of the performance as well as the convergence speed.

NeurIPS Conference 2017 Conference Paper

Triple Generative Adversarial Nets

Chongxuan Li
Taufik Xu
Jun Zhu
Bo Zhang

Generative Adversarial Nets (GANs) have shown promise in image generation and semi-supervised learning (SSL). However, existing GANs in SSL have two problems: (1) the generator and the discriminator (i. e. the classifier) may not be optimal at the same time; and (2) the generator cannot control the semantics of the generated samples. The problems essentially arise from the two-player formulation, where a single discriminator shares incompatible roles of identifying fake samples and predicting labels and it only estimates the data without considering the labels. To address the problems, we present triple generative adversarial net (Triple-GAN), which consists of three players---a generator, a discriminator and a classifier. The generator and the classifier characterize the conditional distributions between images and labels, and the discriminator solely focuses on identifying fake image-label pairs. We design compatible utilities to ensure that the distributions characterized by the classifier and the generator both converge to the data distribution. Our results on various datasets demonstrate that Triple-GAN as a unified model can simultaneously (1) achieve the state-of-the-art classification results among deep generative models, and (2) disentangle the classes and styles of the input and transfer smoothly in the data space via interpolation in the latent space class-conditionally.

ICML Conference 2016 Conference Paper

Learning to Generate with Memory

Chongxuan Li
Jun Zhu 0001
Bo Zhang 0010

Memory units have been widely used to enrich the capabilities of deep networks on capturing long-term dependencies in reasoning and prediction tasks, but little investigation exists on deep generative models (DGMs) which are good at inferring high-level invariant representations from unlabeled data. This paper presents a deep generative model with a possibly large external memory and an attention mechanism to capture the local detail information that is often lost in the bottom-up abstraction process in representation learning. By adopting a smooth attention model, the whole network is trained end-to-end by optimizing a variational bound of data likelihood via auto-encoding variational Bayesian methods, where an asymmetric recognition network is learnt jointly to infer high-level invariant representations. The asymmetric architecture can reduce the competition between bottom-up invariant feature extraction and top-down generation of instance details. Our experiments on several datasets demonstrate that memory can significantly boost the performance of DGMs on various tasks, including density estimation, image generation, and missing value imputation, and DGMs with memory can achieve state-of-the-art quantitative results.

NeurIPS Conference 2015 Conference Paper

Max-Margin Deep Generative Models

Chongxuan Li
Jun Zhu
Tianlin Shi
Bo Zhang

Deep generative models (DGMs) are effective on learning multilayered representations of complex data and performing inference of input data by exploring the generative ability. However, little work has been done on examining or empowering the discriminative ability of DGMs on making accurate predictions. This paper presents max-margin deep generative models (mmDGMs), which explore the strongly discriminative principle of max-margin learning to improve the discriminative power of DGMs, while retaining the generative capability. We develop an efficient doubly stochastic subgradient algorithm for the piecewise linear objective. Empirical results on MNIST and SVHN datasets demonstrate that (1) max-margin learning can significantly improve the prediction performance of DGMs and meanwhile retain the generative ability; and (2) mmDGMs are competitive to the state-of-the-art fully discriminative networks by employing deep convolutional neural networks (CNNs) as both recognition and generative models.