William T. Freeman

TMLR Journal 2026 Journal Article

Denoising Hamiltonian Network for Physical Reasoning

• Congyue Deng
• Brandon Y. Feng
• Cecilia Garraffo
• Alan Garbarz
• Robin Walters
• William T. Freeman
• Leonidas Guibas
• Kaiming He

Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks. While these methods offer theoretical guarantees, they face two key limitations: (i) they primarily model local relations between adjacent time steps, overlooking longer-range or higher-level physical interactions, and (ii) they focus on forward simulation while neglecting broader physical reasoning tasks. We propose the Denoising Hamiltonian Network (DHN), a novel framework that generalizes Hamiltonian mechanics operators into more flexible neural operators. DHN captures non-local temporal relationships and mitigates numerical integration errors through a denoising mechanism. DHN also supports multi-system modeling with a global conditioning mechanism. We demonstrate its effectiveness and flexibility across three diverse physical reasoning tasks with distinct inputs and outputs.

ICLR Conference 2025 Conference Paper

Adaptive Length Image Tokenization via Recurrent Allocation

• Shivam Duggal
• Phillip Isola
• Antonio Torralba 0001
• William T. Freeman

Current vision systems typically assign fixed-length representations to images, regardless of the information content. This contrasts with human intelligence —and even large language models—which allocate varying representational capacities based on entropy, context and familiarity. Inspired by this, we propose an approach to learn variable-length token representations for 2D images. Our encoder-decoder architecture recursively processes 2D image tokens, distilling them into 1D latent tokens over multiple iterations of recurrent rollouts. Each iteration refines the 2D tokens, updates the existing 1D latent tokens, and adaptively increases representational capacity by adding new tokens. This enables compression of images into a variable number of tokens, ranging from 32 to 256. We validate our tokenizer using reconstruction loss and FID metrics, demonstrating that token count aligns with image entropy, familiarity and downstream task requirements. Recurrent token processing with increasing representational capacity in each iteration shows signs of token specialization, revealing potential for object / part discovery.

ICLR Conference 2025 Conference Paper

I-Con: A Unifying Framework for Representation Learning

• Shaden Naif Alshammari
• John R. Hershey
• Axel Feldmann
• William T. Freeman
• Mark Hamilton

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of mod- ern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality re- duction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

ICLR Conference 2025 Conference Paper

RelitLRM: Generative Relightable Radiance for Large Reconstruction Models

• Tianyuan Zhang
• Zhengfei Kuang
• Haian Jin
• Zexiang Xu
• Sai Bi
• Hao Tan 0002
• He Zhang 0004
• Yiwei Hu

We propose RelitLRM, a Large Reconstruction Model (LRM) for generating high-quality Gaussian splatting representations of 3D objects under novel illuminations from sparse (4-8) posed images captured under unknown static lighting. Unlike prior inverse rendering methods requiring dense captures and slow optimization, often causing artifacts like incorrect highlights or shadow baking, RelitLRM adopts a feed-forward transformer-based model with a novel combination of a geometry reconstructor and a relightable appearance generator based on diffusion. The model is trained end-to-end on synthetic multi-view renderings of objects under varying known illuminations. This architecture design enables to effectively decompose geometry and appearance, resolve the ambiguity between material and lighting, and capture the multi-modal distribution of shadows and specularity in the relit appearance. We show our sparse-view feed-forward RelitLRM offers competitive relighting results to state-of-the-art dense-view optimization-based baselines while being significantly faster. Our project page is available at: https://relit-lrm.github.io/.

ICLR Conference 2024 Conference Paper

COCO-Periph: Bridging the Gap Between Human and Machine Perception in the Periphery

• Anne Harrington
• Vasha DuTell
• Mark Hamilton
• Ayush Tewari
• Simon Stent
• William T. Freeman
• Ruth Rosenholtz

Evaluating deep neural networks (DNNs) as models of human perception has given rich insights into both human visual processing and representational properties of DNNs. We extend this work by analyzing how well DNNs perform compared to humans when constrained by peripheral vision -- which limits human performance on a variety of tasks, but also benefits the visual system significantly. We evaluate this by (1) modifying the Texture Tiling Model (TTM), a well tested model of peripheral vision to be more flexibly used with DNNs, (2) generating a large dataset which we call COCO-Periph that contains images transformed to capture the information available in human peripheral vision, and (3) comparing DNNs to humans at peripheral object detection using a psychophysics experiment. Our results show that common DNNs underperform at object detection compared to humans when simulating peripheral vision with TTM. Training on COCO-Periph begins to reduce the gap between human and DNN performance and leads to small increases in corruption robustness, but DNNs still struggle to capture human-like sensitivity to peripheral clutter. Our work brings us closer to accurately modeling human vision, and paves the way for DNNs to mimic and sometimes benefit from properties of human visual processing.

ICLR Conference 2024 Conference Paper

FeatUp: A Model-Agnostic Framework for Features at Any Resolution

• Stephanie Fu
• Mark Hamilton
• Laura E. Brandt
• Axel Feldmann
• Zhoutong Zhang
• William T. Freeman

Deep features are a cornerstone of computer vision research, capturing image semantics and enabling the community to solve downstream tasks even in the zero- or few-shot regime. However, these features often lack the spatial resolution to directly perform dense prediction tasks like segmentation and depth prediction because models aggressively pool information over large areas. In this work, we introduce FeatUp, a task- and model-agnostic framework to restore lost spatial information in deep features. We introduce two variants of FeatUp: one that guides features with high-resolution signal in a single forward pass, and one that fits an implicit model to a single image to reconstruct features at any resolution. Both approaches use a multi-view consistency loss with deep analogies to NeRFs. Our features retain their original semantics and can be swapped into existing applications to yield resolution and performance gains even without re-training. We show that FeatUp significantly outperforms other feature upsampling and image super-resolution approaches in class activation map generation, transfer learning for segmentation and depth prediction, and end-to-end training for semantic segmentation.

NeurIPS Conference 2024 Conference Paper

Improved Distribution Matching Distillation for Fast Image Synthesis

• Tianwei Yin
• Michaël Gharbi
• Taesung Park
• Richard Zhang
• Eli Shechtman
• Frédo Durand
• William T. Freeman

Recent approaches have shown promises distilling expensive diffusion models into efficient one-step generators. Amongst them, Distribution Matching Distillation (DMD) produces one-step generators that match their teacher in distribution, i. e. , the distillation process does not enforce a one-to-one correspondence with the sampling trajectories of their teachers. However, to ensure stable training in practice, DMD requires an additional regression loss computed using a large set of noise--image pairs, generated by the teacher with many steps of a deterministic sampler. This is not only computationally expensive for large-scale text-to-image synthesis, but it also limits the student's quality, tying it too closely to the teacher's original sampling paths. We introduce DMD2, a set of techniques that lift this limitation and improve DMD training. First, we eliminate the regression loss and the need for expensive dataset construction. We show that the resulting instability is due to the "fake" critic not estimating the distribution of generated samples with sufficient accuracy and propose a two time-scale update rule as a remedy. Second, we integrate a GAN loss into the distillation procedure, discriminating between generated samples and real images. This lets us train the student model on real data, thus mitigating the imperfect "real" score estimation from the teacher model, and thereby enhancing quality. Third, we introduce a new training procedure that enables multi-step sampling in the student, andaddresses the training--inference input mismatch of previous work, by simulating inference-time generator samples during training. Taken together, our improvements set new benchmarks in one-step image generation, with FID scores of 1. 28 on ImageNet-64×64 and 8. 35 on zero-shot COCO 2014, surpassing the original teacher despite a 500X reduction in inference cost. Further, we show our approach can generate megapixel images by distilling SDXL, demonstrating exceptional visual quality among few-step methods, and surpassing the teacher. We release our code and pretrained models.

ICLR Conference 2023 Conference Paper

Exploring perceptual straightness in learned visual representations

• Anne Harrington
• Vasha DuTell
• Ayush Tewari
• Mark Hamilton
• Simon Stent
• Ruth Rosenholtz
• William T. Freeman

Humans have been shown to use a ''straightened'' encoding to represent the natural visual world as it evolves in time (Henaff et al. 2019). In the context of discrete video sequences, ''straightened'' means that changes between frames follow a more linear path in representation space at progressively deeper levels of processing. While deep convolutional networks are often proposed as models of human visual processing, many do not straighten natural videos. In this paper, we explore the relationship between network architecture, differing types of robustness, biologically-inspired filtering mechanisms, and representational straightness in response to time-varying input; we identify strengths and limitations of straightness as a useful way of evaluating neural network representations. We find that (1) adversarial training leads to straighter representations in both CNN and transformer-based architectures but (2) this effect is task-dependent, not generalizing to tasks such as segmentation and frame-prediction, where straight representations are not favorable for predictions; and nor to other types of robustness. In addition, (3) straighter representations impart temporal stability to class predictions, even for out-of-distribution data. Finally, (4) biologically-inspired elements increase straightness in the early stages of a network, but do not guarantee increased straightness in downstream layers of CNNs. We show that straightness is an easily computed measure of representational robustness and stability, as well as a hallmark of human representations with benefits for computer vision models.

ICML Conference 2023 Conference Paper

Muse: Text-To-Image Generation via Masked Generative Transformers

• Huiwen Chang
• Han Zhang 0010
• Jarred Barber
• Aaron Maschinot
• José Lezama
• Lu Jiang 0004
• Ming-Hsuan Yang 0001
• Kevin Murphy 0002

We present Muse, a text-to-image Transformermodel that achieves state-of-the-art image genera-tion performance while being significantly moreefficient than diffusion or autoregressive models. Muse is trained on a masked modeling task indiscrete token space: given the text embeddingextracted from a pre-trained large language model(LLM), Muse learns to predict randomly maskedimage tokens. Compared to pixel-space diffusionmodels, such as Imagen and DALL-E 2, Muse issignificantly more efficient due to the use of dis-crete tokens and requires fewer sampling itera-tions; compared to autoregressive models such asParti, Muse is more efficient due to the use of par-allel decoding. The use of a pre-trained LLM en-ables fine-grained language understanding, whichtranslates to high-fidelity image generation andthe understanding of visual concepts such as ob-jects, their spatial relationships, pose, cardinalityetc. Our 900M parameter model achieves a newSOTA on CC3M, with an FID score of 6. 06. TheMuse 3B parameter model achieves an FID of7. 88 on zero-shot COCO evaluation, along with aCLIP score of 0. 32. Muse also directly enables anumber of image editing applications without theneed to fine-tune or invert the model: inpainting, outpainting, and mask-free editing. More resultsand videos demonstrating editing are available at https: //muse-icml. github. io/

ICLR Conference 2023 Conference Paper

Neural Groundplans: Persistent Neural Scene Representations from a Single Image

• Prafull Sharma
• Ayush Tewari
• Yilun Du
• Sergey Zakharov
• Rares Ambrus
• Adrien Gaidon
• William T. Freeman
• Frédo Durand

We present a method to map 2D image observations of a scene to a persistent 3D scene representation, enabling novel view synthesis and disentangled representation of the movable and immovable components of the scene. Motivated by the bird’s-eye-view (BEV) representation commonly used in vision and robotics, we propose conditional neural groundplans, ground-aligned 2D feature grids, as persistent and memory-efficient scene representations. Our method is trained self-supervised from unlabeled multi-view observations using differentiable rendering, and learns to complete geometry and appearance of occluded regions. In addition, we show that we can leverage multi-view videos at training time to learn to separately reconstruct static and movable components of the scene from a single image at test time. The ability to separately reconstruct movable objects enables a variety of downstream tasks using simple heuristics, such as extraction of object-centric 3D representations, novel view synthesis, instance-level segmentation, 3D bounding box prediction, and scene editing. This highlights the value of neural groundplans as a backbone for efficient 3D scene understanding models.

ICLR Conference 2022 Conference Paper

Axiomatic Explanations for Visual Search, Retrieval, and Similarity Learning

• Mark Hamilton
• Scott M. Lundberg
• Stephanie Fu
• Lei Zhang 0001
• William T. Freeman

Visual search, recommendation, and contrastive similarity learning power technologies that impact billions of users worldwide. Modern model architectures can be complex and difficult to interpret, and there are several competing techniques one can use to explain a search engine's behavior. We show that the theory of fair credit assignment provides a unique axiomatic solution that generalizes several existing recommendation- and metric-explainability techniques in the literature. Using this formalism, we show when existing approaches violate "fairness" and derive methods that sidestep these shortcomings and naturally handle counterfactual information. More specifically, we show existing approaches implicitly approximate second-order Shapley-Taylor indices and extend CAM, GradCAM, LIME, SHAP, SBSM, and other methods to search engines. These extensions can extract pairwise correspondences between images from trained opaque-box models. We also introduce a fast kernel-based method for estimating Shapley-Taylor indices that require orders of magnitude fewer function evaluations to converge. Finally, we show that these game-theoretic measures yield more consistent explanations for image similarity architectures.

ICLR Conference 2022 Conference Paper

Unsupervised Semantic Segmentation by Distilling Feature Correspondences

• Mark Hamilton
• Zhoutong Zhang
• Bharath Hariharan
• Noah Snavely
• William T. Freeman

Unsupervised semantic segmentation aims to discover and localize semantically meaningful categories within image corpora without any form of annotation. To solve this task, algorithms must produce features for every pixel that are both semantically meaningful and compact enough to form distinct clusters. Unlike previous works which achieve this with a single end-to-end framework, we propose to separate feature learning from cluster compactification. Empirically, we show that current unsupervised feature learning frameworks already generate dense features whose correlations are semantically consistent. This observation motivates us to design STEGO ($\textbf{S}$elf-supervised $\textbf{T}$ransformer with $\textbf{E}$nergy-based $\textbf{G}$raph $\textbf{O}$ptimization), a novel framework that distills unsupervised features into high-quality discrete semantic labels. At the core of STEGO is a novel contrastive loss function that encourages features to form compact clusters while preserving their association pattern. STEGO yields a significant improvement over the prior state of the art, on both the CocoStuff ($\textbf{+14 mIoU}$) and Cityscapes ($\textbf{+9 mIoU}$) semantic segmentation challenges.

ICLR Conference 2020 Conference Paper

Deep Audio Priors Emerge From Harmonic Convolutional Networks

• Zhoutong Zhang
• Yunyun Wang
• Chuang Gan 0001
• Jiajun Wu 0001
• Joshua B. Tenenbaum
• Antonio Torralba 0001
• William T. Freeman

Convolutional neural networks (CNNs) excel in image recognition and generation. Among many efforts to explain their effectiveness, experiments show that CNNs carry strong inductive biases that capture natural image priors. Do deep networks also have inductive biases for audio signals? In this paper, we empirically show that current network architectures for audio processing do not show strong evidence in capturing such priors. We propose Harmonic Convolution, an operation that helps deep networks distill priors in audio signals by explicitly utilizing the harmonic structure within. This is done by engineering the kernel to be supported by sets of harmonic series, instead of local neighborhoods for convolutional kernels. We show that networks using Harmonic Convolution can reliably model audio priors and achieve high performance in unsupervised audio restoration tasks. With Harmonic Convolution, they also achieve better generalization performance for sound source separation.

ICRA Conference 2019 Conference Paper

ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Robotics

• Yuanming Hu
• Jiancheng Liu
• Andrew Spielberg
• Joshua B. Tenenbaum
• William T. Freeman
• Jiajun Wu 0001
• Daniela Rus
• Wojciech Matusik

Physical simulators have been widely used in robot planning and control. Among them, differentiable simulators are particularly favored, as they can be incorporated into gradient-based optimization algorithms that are efficient in solving inverse problems such as optimal control and motion planning. Therefore, rigid body simulators and recently their differentiable variants are studied extensively. Simulating deformable objects is, however, more challenging compared to rigid body dynamics. The underlying physical laws of deformable objects are more complex, and the resulting systems have orders of magnitude more degrees of freedom and there-fore they are significantly more computationally expensive to simulate. Computing gradients with respect to physical design or controller parameters is typically even more computationally challenging. In this paper, we propose a real-time, differentiable hybrid Lagrangian-Eulerian physical simulator for deformable objects, ChainQueen, based on the Moving Least Squares Material Point Method (MLS-MPM). MLS-MPM can simulate deformable objects with collisions and can be seamlessly incorporated into soft robotic systems. We demonstrate that our simulator achieves high precision in both forward simulation and backward gradient computation. We have successfully employed it in a diverse set of inference, control and co-design tasks for soft robotics.

IROS Conference 2018 Conference Paper

3D Shape Perception from Monocular Vision, Touch, and Shape Priors

• Shaoxiong Wang
• Jiajun Wu 0001
• Xingyuan Sun
• Wenzhen Yuan 0001
• William T. Freeman
• Joshua B. Tenenbaum
• Edward H. Adelson

Perceiving accurate 3D object shape is important for robots to interact with the physical world. Current research along this direction has been primarily relying on visual observations. Vision, however useful, has inherent limitations due to occlusions and the 2D-3D ambiguities, especially for perception with a monocular camera. In contrast, touch gets precise local shape information, though its efficiency for reconstructing the entire shape could be low. In this paper, we propose a novel paradigm that efficiently perceives accurate 3D object shape by incorporating visual and tactile observations, as well as prior knowledge of common object shapes learned from large-scale shape repositories. We use vision first, applying neural networks with learned shape priors to predict an object's 3D shape from a single-view color image. We then use tactile sensing to refine the shape; the robot actively touches the object regions where the visual prediction has high uncertainty. Our method efficiently builds the 3D shape of common objects from a color image and a small number of tactile explorations (around 10). Our setup is easy to apply and has potentials to help robots better perform grasping or manipulation tasks on real-world objects.

UAI Conference 2012 Conference Paper

Exploiting compositionality to explore a large space of model structures

• Roger B. Grosse
• Ruslan Salakhutdinov
• William T. Freeman
• Joshua B. Tenenbaum

The recent proliferation of richly structured probabilistic models raises the question of how to automatically determine an appropriate model for a dataset. We investigate this question for a space of matrix decomposition models which can express a variety of widely used models from unsupervised learning. To enable model selection, we organize these models into a context-free grammar which generates a wide variety of structures through the compositional application of a few simple rules. We use our grammar to generically and efficiently infer latent components and estimate predictive likelihood for nearly 2500 structures using a small toolbox of reusable algorithms. Using a greedy search over our grammar, we automatically choose the decomposition structure from raw data by evaluating only a small fraction of all models. The proposed method typically finds the correct structure for synthetic data and backs off gracefully to simpler models under heavy noise. It learns sensible structures for datasets as diverse as image patches, motion capture, 20 Questions, and U.S. Senate votes, all using exactly the same code.

SODA Conference 2011 Invited Paper

Where computer vision needs help from computer science

• William T. Freeman