Joint KL yields horizon-free approximation but an information-theoretic lower bound of order Omega(H) for estimation error in autoregressive learning, with matching computationally efficient upper bounds.
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Deep Unsupervised Learning using Nonequilibrium Thermodynamics
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abstract
A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm.
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representative citing papers
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
DDIMs construct non-Markovian diffusion processes that share DDPM training objectives but allow much faster reverse sampling, demonstrated empirically at 10-50x wall-clock speedup.
DiffWave is a non-autoregressive diffusion model that generates high-fidelity audio waveforms from noise in constant steps, matching WaveNet vocoder quality while being orders of magnitude faster and outperforming prior models in unconditional generation.
DCGANs with architectural constraints learn a hierarchy of representations from object parts to scenes in both generator and discriminator across image datasets.
Closed-Form Diffusion Policies enable training-free imitation learning by using closed-form scores derived from demonstration data, achieving competitive benchmark performance with millisecond inference and composable editing of pre-trained policies.
LGS pretrained on 2.5M trajectories across 16 systems matches deterministic baselines at one step and halves 20-step error while using far less compute and adapting to held-out higher-resolution flows.
A LoRA-adapted conditional diffusion surrogate for electromagnetic calorimeter showers matches key observables within 2% RMSE and reproduces directional trends in design-utility gradients.
Proposes an advection-diffusion PDE corruption process with stochastic velocity fields and Lattice Boltzmann solver for diffusion models, generalizing prior PDE methods.
Diffusion-QL uses conditional diffusion models as expressive policies in offline RL by coupling behavior cloning with Q-value maximization, achieving SOTA on most D4RL tasks.
A hierarchical prior-decoder model using CLIP latents generates more diverse text-conditional images than direct methods while preserving photorealism and caption fidelity.
Latent diffusion models achieve state-of-the-art inpainting and competitive results on unconditional generation, scene synthesis, and super-resolution by performing the diffusion process in the latent space of pretrained autoencoders with cross-attention conditioning, while cutting computational and
A 3.5-billion-parameter diffusion model with classifier-free guidance generates images preferred over DALL-E by human raters and can be fine-tuned for text-guided inpainting.
SDEdit performs guided image synthesis and editing by adding noise to inputs and refining them via denoising with a diffusion model's SDE prior, outperforming GAN methods in human studies without task-specific training.
Diffusion models with architecture improvements and classifier guidance achieve superior FID scores to GANs on unconditional and conditional ImageNet image synthesis.
21cmEMUv3 emulates the cylindrical 21cm power spectrum via score-based diffusion and six other 21cmFAST observables via LSTM networks at sub-percent accuracy, then uses the emulator to infer a lower limit on soft-band X-ray luminosity from HERA data.
REPA-P aligns intermediate representations in diffusion models with physical states using first-principles PDE residuals to accelerate convergence and boost out-of-distribution robustness on PDE tasks.
A flow-matching generative model trained on CoLBT-hydro data conditionally generates marginal final-state hadron spectra from jet-induced hydro responses in 0-10% Pb+Pb collisions at 5.02 TeV, matching training data statistics with approximately six orders of magnitude computational speedup.
Diffusion LLMs can act as their own efficiency teachers by using revokable parallel decoding to identify reliable token orders and then distilling those orders into the model parameters for faster inference.
Recasts sampling-based nonconvex optimization as smoothed gradient descent to obtain non-asymptotic convergence guarantees and introduces the DIDA annealed algorithm that converges to the global optimum.
PG-3DGS couples 3D Gaussian Splatting with differentiable physics so that optimized shapes satisfy both visual fidelity and physical objectives such as pouring and aerodynamic lift, with real-world 3D-printed validation.
Implicit score matching trains diffusion models that successfully sample SU(3) Wilson gauge configurations on lattices, with a Hamiltonian-dynamics corrector needed for strong coupling.
GCCM prevents shortcut collapse in consistency models for graph prediction by using contrastive negative pairs and input feature perturbation, leading to better performance than deterministic baselines.
FMDiffWA uses frequency-domain modulation inside diffusion sampling to neutralize watermarks in images while preserving visual quality and generalizing across watermarking schemes.
citing papers explorer
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Autoregressive Learning in Joint KL: Sharp Oracle Bounds and Lower Bounds
Joint KL yields horizon-free approximation but an information-theoretic lower bound of order Omega(H) for estimation error in autoregressive learning, with matching computationally efficient upper bounds.
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Generative models on phase space
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
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Denoising Diffusion Implicit Models
DDIMs construct non-Markovian diffusion processes that share DDPM training objectives but allow much faster reverse sampling, demonstrated empirically at 10-50x wall-clock speedup.
-
DiffWave: A Versatile Diffusion Model for Audio Synthesis
DiffWave is a non-autoregressive diffusion model that generates high-fidelity audio waveforms from noise in constant steps, matching WaveNet vocoder quality while being orders of magnitude faster and outperforming prior models in unconditional generation.
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Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks
DCGANs with architectural constraints learn a hierarchy of representations from object parts to scenes in both generator and discriminator across image datasets.
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Training-Free Imitation Learning with Closed-Form Diffusion Policies
Closed-Form Diffusion Policies enable training-free imitation learning by using closed-form scores derived from demonstration data, achieving competitive benchmark performance with millisecond inference and composable editing of pre-trained policies.
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Latent Generative Solvers for Generalizable Long-Term Physics Simulation
LGS pretrained on 2.5M trajectories across 16 systems matches deterministic baselines at one step and halves 20-step error while using far less compute and adapting to held-out higher-resolution flows.
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Differentiable Surrogate for Detector Simulation and Design with Diffusion Models
A LoRA-adapted conditional diffusion surrogate for electromagnetic calorimeter showers matches key observables within 2% RMSE and reproduces directional trends in design-utility gradients.
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Beyond Blur: A Fluid Perspective on Generative Diffusion Models
Proposes an advection-diffusion PDE corruption process with stochastic velocity fields and Lattice Boltzmann solver for diffusion models, generalizing prior PDE methods.
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Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning
Diffusion-QL uses conditional diffusion models as expressive policies in offline RL by coupling behavior cloning with Q-value maximization, achieving SOTA on most D4RL tasks.
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Hierarchical Text-Conditional Image Generation with CLIP Latents
A hierarchical prior-decoder model using CLIP latents generates more diverse text-conditional images than direct methods while preserving photorealism and caption fidelity.
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High-Resolution Image Synthesis with Latent Diffusion Models
Latent diffusion models achieve state-of-the-art inpainting and competitive results on unconditional generation, scene synthesis, and super-resolution by performing the diffusion process in the latent space of pretrained autoencoders with cross-attention conditioning, while cutting computational and
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GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models
A 3.5-billion-parameter diffusion model with classifier-free guidance generates images preferred over DALL-E by human raters and can be fine-tuned for text-guided inpainting.
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SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations
SDEdit performs guided image synthesis and editing by adding noise to inputs and refining them via denoising with a diffusion model's SDE prior, outperforming GAN methods in human studies without task-specific training.
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Diffusion Models Beat GANs on Image Synthesis
Diffusion models with architecture improvements and classifier guidance achieve superior FID scores to GANs on unconditional and conditional ImageNet image synthesis.
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21cmEMUv3: a hybrid diffusion-LSTM emulator of 21cmFAST summary observables
21cmEMUv3 emulates the cylindrical 21cm power spectrum via score-based diffusion and six other 21cmFAST observables via LSTM networks at sub-percent accuracy, then uses the emulator to infer a lower limit on soft-band X-ray luminosity from HERA data.
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Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment
REPA-P aligns intermediate representations in diffusion models with physical states using first-principles PDE residuals to accelerate convergence and boost out-of-distribution robustness on PDE tasks.
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A flow-matching generative model for event-by-event jet-induced hydro response in high-energy heavy-ion collisions
A flow-matching generative model trained on CoLBT-hydro data conditionally generates marginal final-state hadron spectra from jet-induced hydro responses in 0-10% Pb+Pb collisions at 5.02 TeV, matching training data statistics with approximately six orders of magnitude computational speedup.
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Roll Out and Roll Back: Diffusion LLMs are Their Own Efficiency Teachers
Diffusion LLMs can act as their own efficiency teachers by using revokable parallel decoding to identify reliable token orders and then distilling those orders into the model parameters for faster inference.
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Global Convergence of Sampling-Based Nonconvex Optimization through Diffusion-Style Smoothing
Recasts sampling-based nonconvex optimization as smoothed gradient descent to obtain non-asymptotic convergence guarantees and introduces the DIDA annealed algorithm that converges to the global optimum.
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PG-3DGS: Optimizing 3D Gaussian Splatting to Satisfy Physics Objectives
PG-3DGS couples 3D Gaussian Splatting with differentiable physics so that optimized shapes satisfy both visual fidelity and physical objectives such as pouring and aerodynamic lift, with real-world 3D-printed validation.
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Diffusion model for SU(N) gauge theories
Implicit score matching trains diffusion models that successfully sample SU(3) Wilson gauge configurations on lattices, with a Hamiltonian-dynamics corrector needed for strong coupling.
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GCCM: Enhancing Generative Graph Prediction via Contrastive Consistency Model
GCCM prevents shortcut collapse in consistency models for graph prediction by using contrastive negative pairs and input feature perturbation, leading to better performance than deterministic baselines.
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Breaking Watermarks in the Frequency Domain: A Modulated Diffusion Attack Framework
FMDiffWA uses frequency-domain modulation inside diffusion sampling to neutralize watermarks in images while preserving visual quality and generalizing across watermarking schemes.
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Deepfake Detection Generalization with Diffusion Noise
ANL uses diffusion noise prediction and attention to regularize deepfake detectors for better generalization to unseen synthesis methods without added inference cost.
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Discrete Flow Maps
Discrete Flow Maps recast flow map training for discrete domains using simplex geometry to enable single-step text generation from noise and outperform prior discrete flow models.
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MuPPet: Multi-person 2D-to-3D Pose Lifting
MuPPet introduces person encoding, permutation augmentation, and dynamic multi-person attention to outperform prior single- and multi-person 2D-to-3D pose lifting methods on group interaction datasets while improving occlusion robustness.
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Discrete Bayesian Sample Inference for Graph Generation
GraphBSI uses Bayesian Sample Inference as noise-controlled SDEs to generate discrete graphs in one shot, achieving state-of-the-art results on molecular benchmarks Moses and GuacaMol.
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Seed Diffusion: A Large-Scale Diffusion Language Model with High-Speed Inference
Seed Diffusion Preview is a discrete diffusion language model that reaches 2146 tokens per second inference on H20 GPUs with competitive code benchmark performance, establishing a new speed-quality Pareto frontier.
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Characterizing higher-order representations through generative diffusion models explains human decoded neurofeedback performance
NERD uses RL-trained diffusion models on fMRI data to model higher-order uncertainty representations, outperforming controls and linking individual differences to neurofeedback success.
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Scaling Rectified Flow Transformers for High-Resolution Image Synthesis
Biased noise sampling for rectified flows combined with a bidirectional text-image transformer architecture yields state-of-the-art high-resolution text-to-image results that scale predictably with model size.
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Diff-PCR: Diffusion-Based Correspondence Searching in Doubly Stochastic Matrix Space for Point Cloud Registration
Diff-PCR uses a diffusion model to learn denoising directions for refining doubly stochastic correspondence matrices, improving point cloud registration over one-shot normalization methods.
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Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets
Stable Video Diffusion scales latent video diffusion models via text-to-image pretraining, video pretraining on curated data, and high-quality finetuning to produce competitive text-to-video and image-to-video results while enabling motion LoRA and multi-view 3D applications.
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SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis
SDXL improves upon prior Stable Diffusion versions through a larger UNet backbone, dual text encoders, novel conditioning, and a refinement model, producing higher-fidelity images competitive with black-box state-of-the-art generators.
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Shap-E: Generating Conditional 3D Implicit Functions
Shap-E encodes 3D assets into implicit function parameters then uses a conditional diffusion model to generate new ones from text, enabling fast multi-representation 3D asset creation.
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VideoGPT: Video Generation using VQ-VAE and Transformers
VideoGPT generates competitive natural videos by learning discrete latents with VQ-VAE and modeling them autoregressively with a transformer.
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Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed
Denoising Student distills the multi-step denoising process of score-based and diffusion models into a single forward pass, matching GAN sampling speed while producing comparable sample quality on CIFAR-10, CelebA, and 256x256 LSUN.
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Learning Climate Variability from Scarce Data with Diffusion Models: A Test Case for ENSO
Diffusion models recover known ENSO variability structure from synthetic LIM data when given enough samples, but require pre-training on CMIP6 plus fine-tuning to match observations with the ~700 samples available in ERSSTv5.
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Diffusion-based Denoising Beats Vanilla Score Matching in Parameter Estimation: A Theoretical Explanation
Diffusion-based denoising score matching avoids the mode-separation degradation that affects vanilla score matching error bounds, via suitable hyperparameter choice.
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Mesh Based Simulations with Spatial and Temporal awareness
A unified training framework for mesh-based ML surrogates in CFD improves accuracy and long-horizon stability by enforcing spatial derivative consistency via multi-node prediction, using temporal cross-attention correction, and adding 3D rotary positional embeddings.
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C$^2$FG: Control Classifier-Free Guidance via Score Discrepancy Analysis
C²FG provides a time-dependent guidance controller for diffusion models derived from score discrepancy upper bounds, implemented as an exponential decay function without retraining.
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AdaCorrection: Adaptive Offset Cache Correction for Accurate Diffusion Transformers
AdaCorrection adaptively corrects offset caches in DiT inference via on-the-fly spatio-temporal validity checks to maintain near-original FID with moderate acceleration.
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Towards Generative Location Awareness for Disaster Response: A Probabilistic Cross-view Geolocalization Approach
ProbGLC unifies probabilistic and deterministic geolocalization models to deliver state-of-the-art accuracy (0.86 Acc@1km) plus uncertainty quantification on multi-disaster cross-view datasets.
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BRAIN: Bias-Mitigation Continual Learning Approach to Vision-Brain Understanding
BRAIN uses bias-mitigation continual learning with a new de-bias contrastive loss and angular forgetting mitigation to achieve SOTA performance on vision-brain understanding benchmarks despite brain signal inconsistencies across sessions.
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The Serial Scaling Hypothesis
The serial scaling hypothesis formalizes inherently serial problems in complexity theory and demonstrates that diffusion models cannot solve them.
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Exploring the flavor structure of leptons via diffusion models
Applies diffusion models to generate 10,000 neutrino mass matrices consistent with oscillation parameters in a seesaw model, revealing non-trivial distributions in CP phases and 0νββ effective mass.
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Dual-Stream EEG Decoding for 3D Visual Perception
Dual-stream EEG decoder separates identity and orientation to support 3D reconstruction from neural signals via circular regression and conditioned diffusion.
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Generating Satellite Imagery Data for Wildfire Detection through Mask-Conditioned Generative AI
A pre-trained Earth Observation diffusion model generates realistic post-wildfire Sentinel-2 imagery from burn masks via inpainting, achieving Burn IoU 0.456 and improved saliency over full generation.
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A Review of Diffusion-based Simulation-Based Inference: Foundations and Applications in Non-Ideal Data Scenarios
A synthesis of diffusion-based simulation-based inference methods that address model misspecification, irregular observations, and missing data in scientific applications.
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Sora: A Review on Background, Technology, Limitations, and Opportunities of Large Vision Models
The paper reviews the background, technology, applications, limitations, and future directions of OpenAI's Sora text-to-video generative model based on public information.