mlsanityData to 14 Oct 2026

LEAPS: A discrete neural sampler via locally equivariant networks

arXiv 2502.10843 ↗First posted 15 Feb 2025cs.LG stat.CO stat.MLcited by 31

Not on the map. Why?

Abstract (arXiv)

We propose "LEAPS", an algorithm to sample from discrete distributions known up to normalization by learning a rate matrix of a continuous-time Markov chain (CTMC). LEAPS can be seen as a continuous-time formulation of annealed importance sampling and sequential Monte Carlo methods, extended so that the variance of the importance weights is offset by the inclusion of the CTMC. To derive these importance weights, we introduce a set of Radon-Nikodym derivatives of CTMCs over their path measures. Because the computation of these weights is intractable with standard neural network parameterizations of rate matrices, we devise a new compact representation for rate matrices via what we call "locally equivariant" functions. To parameterize them, we introduce a family of locally equivariant multilayer perceptrons, attention layers, and convolutional networks, and provide an approach to make deep networks that preserve the local equivariance. This property allows us to propose a scalable training algorithm for the rate matrix such that the variance of the importance weights associated to the CTMC are minimal. We demonstrate the efficacy of LEAPS on problems in statistical physics.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). Builds on 35 of its 55 references that are in the map. First posted on arXiv 15 Feb 2025.

Builds on

35 of 55 references.

References · 35

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  3. 2022Flow Matching for Generative Modelingcited by 5,702
  4. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  5. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  6. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  7. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  8. 2024Simple and Effective Masked Diffusion Language Modelscited by 848
  9. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
  10. 2024Simplified and Generalized Masked Diffusion for Discrete Datacited by 626
  11. 2022A Continuous Time Framework for Discrete Denoising Modelscited by 451
  12. 2019General E(2)-Equivariant Steerable CNNscited by 446
23 more
  1. 2024Discrete Flow Matchingcited by 317
  2. 2024Generative Flows on Discrete State-Spaces: Enabling Multimodal Flows with Applications to Protein Co-Designcited by 305
  3. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 181
  4. 2023Protein Design with Guided Discrete Diffusioncited by 157
  5. 2023Denoising Diffusion Samplerscited by 149
  6. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 148
  7. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 116
  8. 2023Improved sampling via learned diffusionscited by 104
  9. 2018Solving Statistical Mechanics Using Variational Autoregressive Networkscited by 100
  10. 2021Annealed Flow Transport Monte Carlocited by 90
  11. 2024Generator Matching: Generative modeling with arbitrary Markov processescited by 86
  12. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 82
  13. 2024NETS: A Non-Equilibrium Transport Samplercited by 69
  14. 2019Discrete Flows: Invertible Generative Models of Discrete Datacited by 68
  15. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  16. 2024A Diffusion Model Framework for Unsupervised Neural Combinatorial Optimizationcited by 59
  17. 2024Flow Matching with General Discrete Paths: A Kinetic-Optimal Perspectivecited by 57
  18. 2023Learning Interpolations between Boltzmann Densitiescited by 43
  19. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physicscited by 29
  20. 2024Liouville Flow Importance Samplercited by 25
  21. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  22. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 20
  23. 2024Discrete generative diffusion models without stochastic differential equations: a tensor network approachcited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 16; 2026: 15.

31 papers.

Sort:

By area:

  1. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 85
  2. 2025Any-Order Flexible Length Masked Diffusioncited by 51
  3. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 23
  4. 2025Tilt Matching for Scalable Sampling and Fine-Tuningcited by 22
  5. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 21
  6. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  7. 2025RNE: plug-and-play diffusion inference-time control and energy-based trainingcited by 17
  8. 2025Proximal Diffusion Neural Samplercited by 16
  9. 2025Inference-Time Scaling of Discrete Diffusion Models via Importance Weighting and Optimal Proposal Designcited by 14
  10. 2025Discrete Neural Flow Samplers with Locally Equivariant Transformercited by 13
  11. 2025CREPE: Controlling Diffusion with Replica Exchangecited by 11
  12. 2026Discrete Feynman-Kac Correctorscited by 11
19 more
  1. 2026Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matchingcited by 10
  2. 2025RETRO SYNFLOW: Discrete Flow Matching for Accurate and Diverse Single-Step Retrosynthesiscited by 6
  3. 2026Scaling Autoregressive Models for Lattice Thermodynamicscited by 5
  4. 2026Flow Sampling: Learning to Sample from Unnormalized Densities via Denoising Conditional Processescited by 5
  5. 2026Contrastive Distribution Matching for Amortized Sequential Monte Carlo in Discrete Diffusioncited by 5
  6. 2026Discrete Adjoint Schr"odinger Bridge Samplercited by 4
  7. 2025Energy-based generator matching: A neural sampler for general state spacecited by 3
  8. 2025Sampling from Energy distributions with Target Concrete Score Identitycited by 3
  9. 2026Discrete diffusion samplers and bridges: Off-policy algorithms and applications in latent spacescited by 2
  10. 2026A2D2: Fine-Tuning Any-Length Discrete Diffusion for Adaptive Decodingcited by 2
  11. 2026Free energy Estimation on Any State Spacecited by 1
  12. 2026FrOGS: Discrete Neural Sampler for Independent Alloy Configurations Across Chemical Conditionscited by 1
  13. 2026FluxLite: Inference-Time Proposal Control for Discrete Diffusion Modelscited by 1
  14. 2025Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Spacecited by 0
  15. 2025Particle Monte Carlo methods for Lattice Field Theorycited by 0
  16. 2026Boltzmann Reinforcement Learning for Noise resilience in Analog Ising Machinescited by 0
  17. 2026Stochastic Counterdiabatic Driving via Biorthogonal Liouvillian Eigenmodescited by 0
  18. 2026Iterative Exact Discrete Guidance for Energy-Based Samplingcited by 0
  19. 2026Fixed-point neural samplers on discrete spacescited by 0