mlsanityData to 14 Oct 2026

Equilibrium Matching: Generative Modeling with Implicit Energy-Based Models

arXiv 2510.02300 ↗First posted 2 Oct 2025cs.LG cs.AI cs.CVcited by 21

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Abstract (arXiv)

We introduce Equilibrium Matching (EqM), a generative modeling framework built from an equilibrium dynamics perspective. EqM discards the non-equilibrium, time-conditional dynamics in traditional diffusion and flow-based generative models and instead learns the equilibrium gradient of an implicit energy landscape. Through this approach, we can adopt an optimization-based sampling process at inference time, where samples are obtained by gradient descent on the learned landscape with adjustable step sizes, adaptive optimizers, and adaptive compute. EqM surpasses the generation performance of diffusion/flow models empirically, achieving an FID of 1.90 on ImageNet 256×256. EqM is also theoretically justified to learn and sample from the data manifold. Beyond generation, EqM is a flexible framework that naturally handles tasks including partially noised image denoising, OOD detection, and image composition. By replacing time-conditional velocities with a unified equilibrium landscape, EqM offers a tighter bridge between flow and energy-based models and a simple route to optimization-driven inference.

Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). Builds on 30 of its 39 references that are in the map. First posted on arXiv 2 Oct 2025.

Builds on

30 of 39 references.

References · 30

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,713
  3. 2020Denoising Diffusion Implicit Modelscited by 9,781
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  5. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  6. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  7. 2022Scalable Diffusion Models with Transformerscited by 6,054
  8. 2022Flow Matching for Generative Modelingcited by 5,702
  9. 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,761
  10. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  11. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  12. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,979
18 more
  1. 2018Glow: Generative Flow with Invertible 1x1 Convolutionscited by 1,545
  2. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  3. 2024SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformerscited by 737
  4. 2022StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasetscited by 492
  5. 2017PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modificationscited by 417
  6. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 405
  7. 2023Understanding Diffusion Objectives as the ELBO with Simple Data Augmentationcited by 304
  8. 2024Flow Matching Guide and Codecited by 301
  9. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 220
  10. 2016A Theory of Generative ConvNetcited by 174
  11. 2020Improved Contrastive Divergence Training of Energy Based Modelscited by 130
  12. 2020Learning Energy-Based Models by Diffusion Recovery Likelihoodcited by 123
  13. 2019On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Modelscited by 105
  14. 2025Diffuse and Disperse: Image Generation with Representation Regularizationcited by 70
  15. 2025Is Noise Conditioning Necessary for Denoising Generative Models?cited by 44
  16. 2025Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modelingcited by 27
  17. 2023Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approachcited by 18
  18. 2018Generative Modeling by Inclusive Neural Random Fields with Applications in Image Generation and Anomaly Detectioncited by 9

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 18.

21 papers.

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  1. 2025Diffusion Models in Simulation-Based Inference: A Tutorial Reviewcited by 11
  2. 2026Blind denoising diffusion models and the blessings of dimensionalitycited by 9
  3. 2026The Geometry of Noise: Why Diffusion Models Don't Need Noise Conditioningcited by 8
  4. 2025Think Consistently, Reason Efficiently: Energy-Based Calibration for Implicit Chain-of-Thoughtcited by 4
  5. 2025Speedrunning ImageNet Diffusioncited by 3
  6. 2026Generative Control as Optimization: Time Unconditional Flow Matching for Adaptive and Robust Robotic Controlcited by 3
  7. 2026π0-EqM: Equilibrium Matching for Closed-Loop Vision-Language-Action Controlcited by 3
  8. 2026DVD: Discrete Voxel Diffusion for 3D Generation and Editingcited by 2
  9. 2026What Time Is It? How Data Geometry Makes Time Conditioning Optional for Flow Matchingcited by 2
  10. 2026Beckmann Transport Models: From Autonomous Flows to One-Step Mapscited by 2
  11. 2026Generative Pseudo-Force Fields for Molecular Generationcited by 1
  12. 2026Equilibrium Forcing: Adaptive Video Generation Without Noise Conditioningcited by 1
9 more
  1. 2026Conditional Denoising Model as a Physical Surrogate Modelcited by 0
  2. 2026Distance Marching for Generative Modelingcited by 0
  3. 2026TerraBind: Fast and Accurate Binding Affinity Prediction through Coarse Structural Representationscited by 0
  4. 2026Recovering Hidden Reward in Diffusion-Based Policiescited by 0
  5. 2026Generating Physically Consistent Molecules with Energy-Based Modelscited by 0
  6. 2026Advancing Optimal Subset Oracle via Learning Relaxation of Neural Set Functionscited by 0
  7. 2026Does Uniform Discrete Diffusion Need Time?cited by 0
  8. 2026Jumping up and down: Denoiser diffusion models for discrete ordinal datacited by 0
  9. 2026PotentialEP: Backprop-Free Training of CIFAR-Scale Generative Models via Equilibrium Propagationcited by 0