mlsanityData to 7 Oct 2026

Oops I Took A Gradient: Scalable Sampling for Discrete Distributions

arXiv 2102.04509 ↗First posted 8 Feb 2021cs.LGcited by 92

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Abstract (arXiv)

We propose a general and scalable approximate sampling strategy for probabilistic models with discrete variables. Our approach uses gradients of the likelihood function with respect to its discrete inputs to propose updates in a Metropolis-Hastings sampler. We show empirically that this approach outperforms generic samplers in a number of difficult settings including Ising models, Potts models, restricted Boltzmann machines, and factorial hidden Markov models. We also demonstrate the use of our improved sampler for training deep energy-based models on high dimensional discrete data. This approach outperforms variational auto-encoders and existing energy-based models. Finally, we give bounds showing that our approach is near-optimal in the class of samplers which propose local updates.

Key facts. Cited by 92 papers in the map (data through 7 Oct 2026). Builds on 18 of its 47 references that are in the map. First posted on arXiv 8 Feb 2021.

Builds on

18 of 47 references.

References · 18

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  3. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  4. 2013Auto-Encoding Variational Bayescited by 3,980
  5. 2016The Concrete Distribution: A Continuous Relaxation of Discrete Random Variablescited by 1,135
  6. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 498
  7. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 402
  8. 2017VAE with a VampPriorcited by 247
  9. 2019On the Anatomy of MCMC-Based Maximum Likelihood Learning of Energy-Based Modelscited by 105
  10. 2020Residual Energy-Based Models for Text Generationcited by 95
  11. 2020No MCMC for me: Amortized sampling for fast and stable training of energy-based modelscited by 64
  12. 2020Stochastic Security: Adversarial Defense Using Long-Run Dynamics of Energy-Based Modelscited by 58
6 more
  1. 2014Accurate and Conservative Estimates of MRF Log-likelihood using Reverse Annealingcited by 18
  2. 2015The Hamming Ball Samplercited by 16
  3. 2020Stein Variational Inference for Discrete Distributionscited by 16
  4. 2021Joint Energy-based Model Training for Better Calibrated Natural Language Understanding Modelscited by 14
  5. 2018Stein Variational Gradient Descent Without Gradientcited by 12
  6. 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 7 Oct)

Citing papers per year: 2021: 11; 2022: 19; 2023: 17; 2024: 13; 2025: 19; 2026: 13.

92 papers.

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  1. 2021Flow Network based Generative Models for Non-Iterative Diverse Candidate Generationcited by 384
  2. 2021GFlowNet Foundationscited by 286
  3. 2021Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Modelscited by 251
  4. 2022Trajectory balance: Improved credit assignment in GFlowNetscited by 244
  5. 2023Automatically Auditing Large Language Models via Discrete Optimizationcited by 187
  6. 2024Simple Guidance Mechanisms for Discrete Diffusion Modelscited by 148
  7. 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 144
  8. 2024Unlocking Guidance for Discrete State-Space Diffusion and Flow Modelscited by 124
  9. 2022Generative Flow Networks for Discrete Probabilistic Modelingcited by 113
  10. 2021Unleashing Transformers: Parallel Token Prediction with Discrete Absorbing Diffusion for Fast High-Resolution Image Generation from Vector-Quantized Codescited by 71
  11. 2024Informed Correctors for Discrete Diffusion Modelscited by 57
  12. 2022Differentiable DAG Samplingcited by 46
38 more
  1. 2022A Langevin-like Sampler for Discrete Distributionscited by 42
  2. 2024Compositional Generative Modeling: A Single Model is Not All You Needcited by 41
  3. 2021Exposing the Implicit Energy Networks behind Masked Language Models via Metropolis--Hastingscited by 37
  4. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  5. 2025CANDI: Hybrid Discrete-Continuous Diffusion Modelscited by 31
  6. 2022Particle algorithms for maximum likelihood training of latent variable modelscited by 26
  7. 2025Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modelingcited by 25
  8. 2022Discrete Langevin Sampler via Wasserstein Gradient Flowcited by 23
  9. 2022Gradient Estimation with Discrete Stein Operatorscited by 22
  10. 2023Improving Protein Optimization with Smoothed Fitness Landscapescited by 20
  11. 2022Plug & Play Directed Evolution of Proteins with Gradient-based Discrete MCMCcited by 17
  12. 2025CtrlDiff: Boosting Large Diffusion Language Models with Dynamic Block Prediction and Controllable Generationcited by 17
  13. 2025Discrete Neural Flow Samplers with Locally Equivariant Transformercited by 13
  14. 2022Learning Neural Set Functions Under the Optimal Subset Oraclecited by 10
  15. 2022Enhanced gradient-based MCMC in discrete spacescited by 10
  16. 2025Regularized Langevin Dynamics for Combinatorial Optimizationcited by 10
  17. 2021Perturb-and-max-product: Sampling and learning in discrete energy-based modelscited by 9
  18. 2022Optimal Scaling for Locally Balanced Proposals in Discrete Spacescited by 9
  19. 2023Masked Bayesian Neural Networks : Theoretical Guarantee and its Posterior Inferencecited by 9
  20. 2023Energy Discrepancies: A Score-Independent Loss for Energy-Based Modelscited by 9
  21. 2024Gradient-based Discrete Sampling with Automatic Cyclical Schedulingcited by 9
  22. 2024Generative AI for Controllable Protein Sequence Design: A Surveycited by 8
  23. 2021LSB: Local Self-Balancing MCMC in Discrete Spacescited by 7
  24. 2023Efficient Informed Proposals for Discrete Distributions via Newton's Series Approximationcited by 7
  25. 2023Delta-AI: Local objectives for amortized inference in sparse graphical modelscited by 7
  26. 2022Gradient-Guided Importance Sampling for Learning Binary Energy-Based Modelscited by 6
  27. 2024Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Samplingcited by 6
  28. 2025Reheated Gradient-based Discrete Sampling for Combinatorial Optimizationcited by 6
  29. 2022Statistical applications of contrastive learningcited by 5
  30. 2024Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spacescited by 5
  31. 2021Variational Gibbs Inference for Statistical Model Estimation from Incomplete Datacited by 4
  32. 2023Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithmscited by 4
  33. 2023Structured Voronoi Samplingcited by 4
  34. 2023Gradient-Informed Quality Diversity for the Illumination of Discrete Spacescited by 4
  35. 2023Generative Marginalization Modelscited by 4
  36. 2023Principled Gradient-based Markov Chain Monte Carlo for Text Generationcited by 4
  37. 2025A Variational Perspective on Generative Protein Fitness Optimizationcited by 4
  38. 2025Gradient GA: Gradient Genetic Algorithm for Drug Molecular Designcited by 4

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