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Zehao Dou

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4 papers

2 author rows

ICLR Conference 2025 Conference Paper

Diffusion Transformer Captures Spatial-Temporal Dependencies: A Theory for Gaussian Process Data

Hengyu Fu
Zehao Dou
Jiawei Guo
Mengdi Wang 0001
Minshuo Chen

Diffusion Transformer, the backbone of Sora for video generation, successfully scales the capacity of diffusion models, pioneering new avenues for high-fidelity sequential data generation. Unlike static data such as images, sequential data consists of consecutive data frames indexed by time, exhibiting rich spatial and temporal dependencies. These dependencies represent the underlying dynamic model and are critical to validate the generated data. In this paper, we make the first theoretical step towards bridging diffusion transformers for capturing spatial-temporal dependencies. Specifically, we establish score approximation and distribution estimation guarantees of diffusion transformers for learning Gaussian process data with covariance functions of various decay patterns. We highlight how the spatial-temporal dependencies are captured and affect learning efficiency. Our study proposes a novel transformer approximation theory, where the transformer acts to unroll an algorithm. We support our theoretical results by numerical experiments, providing strong evidence that spatial-temporal dependencies are captured within attention layers, aligning with our approximation theory.

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NeurIPS Conference 2025 Conference Paper

Is Your Diffusion Model Actually Denoising?

Daniel Pfrommer
Zehao Dou
Christopher Scarvelis
Max Simchowitz
Ali Jadbabaie

We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that when these models are queried conditionally, their generations consistently deviate from the idealized "denoising" process upon which diffusion models are formulated, inducing disagreement between popular sampling algorithms (e. g. DDPM, DDIM). We introduce Schedule Deviation, a rigorous measure which captures the rate of deviation from a standard denoising process, and provide a methodology to compute it. Crucially, we demonstrate that the deviation from an idealized denoising process occurs irrespective of the model capacity or amount of training data. We posit that this phenomenon occurs due to the difficulty of bridging distinct denoising flows across different parts of the conditioning space and show theoretically how such a phenomenon can arise through an inductive bias towards smoothness.

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ICLR Conference 2024 Conference Paper

Diffusion Posterior Sampling for Linear Inverse Problem Solving: A Filtering Perspective

Zehao Dou
Yang Song

Diffusion models have achieved tremendous success in generating high-dimensional data like images, videos and audio. These models provide powerful data priors that can solve linear inverse problems in zero shot through Bayesian posterior sampling. However, exact posterior sampling for diffusion models is intractable. Current solutions often hinge on approximations that are either computationally expensive or lack strong theoretical guarantees. In this work, we introduce an efficient diffusion sampling algorithm for linear inverse problems that is guaranteed to be asymptotically accurate. We reveal a link between Bayesian posterior sampling and Bayesian filtering in diffusion models, proving the former as a specific instance of the latter. Our method, termed filtering posterior sampling, leverages sequential Monte Carlo methods to solve the corresponding filtering problem. It seamlessly integrates with all Markovian diffusion samplers, requires no model re-training, and guarantees accurate samples from the Bayesian posterior as particle counts rise. Empirical tests demonstrate that our method generates better or comparable results than leading zero-shot diffusion posterior samplers on tasks like image inpainting, super-resolution, and deblurring.

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ICML Conference 2024 Conference Paper

Theory of Consistency Diffusion Models: Distribution Estimation Meets Fast Sampling

Zehao Dou
Minshuo Chen
Mengdi Wang 0001
Zhuoran Yang

Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive number of steps involved. In response, consistency models have been developed to merge multiple steps in the sampling process, thereby significantly boosting the speed of sample generation without compromising quality. This paper contributes towards the first statistical theory for consistency models, formulating their training as a distribution discrepancy minimization problem. Our analysis yields statistical estimation rates based on the Wasserstein distance for consistency models, matching those of vanilla diffusion models. Additionally, our results encompass the training of consistency models through both distillation and isolation methods, demystifying their underlying advantage.

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