mlsanityData to 7 Oct 2026

Stochastic Optimal Control Matching

arXiv 2312.02027 ↗First posted 4 Dec 2023math.OC cs.LG cs.NAcited by 39

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Abstract (arXiv)

Stochastic optimal control, which has the goal of driving the behavior of noisy systems, is broadly applicable in science, engineering and artificial intelligence. Our work introduces Stochastic Optimal Control Matching (SOCM), a novel Iterative Diffusion Optimization (IDO) technique for stochastic optimal control that stems from the same philosophy as the conditional score matching loss for diffusion models. That is, the control is learned via a least squares problem by trying to fit a matching vector field. The training loss, which is closely connected to the cross-entropy loss, is optimized with respect to both the control function and a family of reparameterization matrices which appear in the matching vector field. The optimization with respect to the reparameterization matrices aims at minimizing the variance of the matching vector field. Experimentally, our algorithm achieves lower error than all the existing IDO techniques for stochastic optimal control for three out of four control problems, in some cases by an order of magnitude. The key idea underlying SOCM is the path-wise reparameterization trick, a novel technique that may be of independent interest. Code at https://github.com/facebookresearch/SOC-matching

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 29 of its 88 references that are in the map. First posted on arXiv 4 Dec 2023.

Builds on

29 of 88 references.

References · 29

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
  3. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  4. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  5. 2018Neural Ordinary Differential Equationscited by 3,733
  6. 2015Variational Inference with Normalizing Flowscited by 2,161
  7. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  8. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  9. 2017Solving high-dimensional partial differential equations using deep learningcited by 549
  10. 2020Scalable Gradients for Stochastic Differential Equationscited by 264
  11. 2016Safe and Efficient Off-Policy Reinforcement Learningcited by 260
  12. 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 188
17 more
  1. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  2. 2021Neural SDEs as Infinite-Dimensional GANscited by 159
  3. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  4. 2023Denoising Diffusion Samplerscited by 144
  5. 2023Improved sampling via learned diffusionscited by 103
  6. 2017Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inferencecited by 97
  7. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 80
  8. 2020Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learningcited by 77
  9. 2022Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Pathscited by 36
  10. 2019Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: II -- The Finite Horizon Casecited by 34
  11. 2017Deep Relaxation: partial differential equations for optimizing deep neural networkscited by 27
  12. 2021Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networkscited by 27
  13. 2015Adaptive importance sampling for control and inferencecited by 23
  14. 2021A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Findingcited by 18
  15. 2019Deep Fictitious Play for Finding Markovian Nash Equilibrium in Multi-Agent Gamescited by 16
  16. 2016High-Dimensional Stochastic Optimal Control using Continuous Tensor Decompositionscited by 13
  17. 2019Variational approach to rare event simulation using least-squares regressioncited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 7; 2025: 14; 2026: 18.

39 papers.

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  1. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 222
  2. 2024Sequential Controlled Langevin Diffusionscited by 47
  3. 2024ResearchTown: Simulator of Human Research Communitycited by 35
  4. 2026Q-learning with Adjoint Matchingcited by 33
  5. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 22
  6. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spacescited by 16
  7. 2025Proximal Diffusion Neural Samplercited by 16
  8. 2025Conditioning Diffusions Using Malliavin Calculuscited by 15
  9. 2025Enhancing Reasoning for Diffusion LLMs via Distribution Matching Policy Optimizationcited by 15
  10. 2025Value Gradient Guidance for Flow Matching Alignmentcited by 14
  11. 2024A Taxonomy of Loss Functions for Stochastic Optimal Controlcited by 11
  12. 2026Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matchingcited by 7
27 more
  1. 2025Deep Learning for Continuous-Time Stochastic Control with Jumpscited by 6
  2. 2025Control Consistency Losses for Diffusion Bridgescited by 6
  3. 2025A brief review of the Deep BSDE method for solving high-dimensional partial differential equationscited by 5
  4. 2025Iterative Tilting for Diffusion Fine-Tuningcited by 4
  5. 2026Discrete Adjoint Schr"odinger Bridge Samplercited by 4
  6. 2026Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Controlcited by 4
  7. 2026Scalable Maximum Entropy Reinforcement Learning for Diffusion Policies via Adjoint Matchingcited by 4
  8. 2024Conditional Lagrangian Wasserstein Flow for Time Series Imputationcited by 3
  9. 2025High-dimensional Mean-Field Games by Particle-based Flow Matchingcited by 3
  10. 2026Supervised Guidance Training for Infinite-Dimensional Diffusion Modelscited by 3
  11. 2026Trust Region Q Adjoint Matchingcited by 3
  12. 2025Flow-based generative models as iterative algorithms in probability spacecited by 2
  13. 2026Improved Constrained Generation by Bridging Pretrained Generative Modelscited by 2
  14. 2026Inference-Time Attribute Distribution Alignment for Unconditional Diffusioncited by 2
  15. 2026Unsupervised Diffusion Solver for Combinatorial Optimization via Combinatorial Adjoint Matchingcited by 2
  16. 2024An Efficient On-Policy Deep Learning Framework for Stochastic Optimal Controlcited by 1
  17. 2025Stein Diffusion Guidance: Training-Free Posterior Correction for Sampling Beyond High-Density Regionscited by 1
  18. 2025HOTA: Hamiltonian framework for Optimal Transport Advectioncited by 1
  19. 2026A unified perspective on fine-tuning and sampling with diffusion and flow modelscited by 1
  20. 2026Twisted Schr"odinger Bridge Matchingcited by 1
  21. 2025Error Propagation in Dynamic Programming: From Stochastic Control to American Option Pricingcited by 0
  22. 2026Minimal-Action Discrete Schr"odinger Bridge Matching for Peptide Sequence Designcited by 0
  23. 2026CMAD: Cooperative Multi-Agent Diffusion via Stochastic Optimal Controlcited by 0
  24. 2026A Schr"odinger Eigenfunction Method for Long-Horizon Stochastic Optimal Controlcited by 0
  25. 2026The Diffusion Encodercited by 0
  26. 2026Path Integral Value Matching for Linear Quadratic Stochastic Optimal Controlcited by 0
  27. 2026Tilted Schr"odinger Bridge Matchingcited by 0

Similar, not cited

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  1. 2024Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence
  2. 2026Diffusion Controller: Framework, Algorithms and Parameterization
  3. 2026Efficient Adjoint Matching for Fine-tuning Diffusion Models
  4. 2026Lyapunov Stability of Stochastic Vector Optimization: Theory and Numerical Implementation ↗
  5. 2025Adaptive Diffusion Guidance via Stochastic Optimal Control
  6. 2026Flow Matching Policy Optimization with Mirror Descent and Entropy Constraints
  7. 2024Denoising Diffusion-Based Control of Nonlinear Systems
  8. 2026Stochastic Optimal Control Sampling for Diffusion Inverse Problems