mlsanityData to 7 Oct 2026

Scalable Gradients for Stochastic Differential Equations

arXiv 2001.01328 ↗First posted 5 Jan 2020cs.LG cs.NA math.NAcited by 264

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Cited by 29 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients with high-order adaptive solvers. Specifically, we derive a stochastic differential equation whose solution is the gradient, a memory-efficient algorithm for caching noise, and conditions under which numerical solutions converge. In addition, we combine our method with gradient-based stochastic variational inference for latent stochastic differential equations. We use our method to fit stochastic dynamics defined by neural networks, achieving competitive performance on a 50-dimensional motion capture dataset.

Key facts. Cited by 264 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Jan 2020.

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Citing papers per year: 2021: 52; 2022: 36; 2023: 41; 2024: 41; 2025: 53; 2026: 41.

264 papers.

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  1. 2022Diffusion Models in Vision: A Surveycited by 1,008
  2. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 835
  3. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 670
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  6. 2021GRAND: Graph Neural Diffusioncited by 258
  7. 2021A Variational Perspective on Diffusion-Based Generative Models and Score Matchingcited by 182
  8. 2021Path Integral Sampler: a stochastic control approach for samplingcited by 175
  9. 2022An optimal control perspective on diffusion-based generative modelingcited by 145
  10. 2024Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Controlcited by 136
  11. 2022Riemannian Diffusion Modelscited by 120
  12. 2021Modeling Irregular Time Series with Continuous Recurrent Unitscited by 101
38 more
  1. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 94
  2. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 87
  3. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  4. 2021Diffusion Normalizing Flowcited by 77
  5. 2021Closed-form Continuous-time Neural Modelscited by 65
  6. 2022Manifold Interpolating Optimal-Transport Flows for Trajectory Inferencecited by 63
  7. 2021Neural ODE Processescited by 57
  8. 2022Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environmentscited by 54
  9. 2023Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEscited by 48
  10. 2021Neural Controlled Differential Equations for Online Prediction Taskscited by 46
  11. 2021Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamicscited by 46
  12. 2023A Computational Framework for Solving Wasserstein Lagrangian Flowscited by 43
  13. 2021MALI: A memory efficient and reverse accurate integrator for Neural ODEscited by 42
  14. 2021Heavy Ball Neural Ordinary Differential Equationscited by 42
  15. 2023Generalized Schr"odinger Bridge Matchingcited by 40
  16. 2021Continuous-Time Model-Based Reinforcement Learningcited by 39
  17. 2022Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusioncited by 39
  18. 2023Stochastic Optimal Control Matchingcited by 39
  19. 2021Infinitely Deep Bayesian Neural Networks with Stochastic Differential Equationscited by 38
  20. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 37
  21. 2022Deep Latent State Space Models for Time-Series Generationcited by 37
  22. 2021Differentiable Annealed Importance Sampling and the Perils of Gradient Noisecited by 36
  23. 2023DiffAttack: Evasion Attacks Against Diffusion-Based Adversarial Purificationcited by 36
  24. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 35
  25. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  26. 2023Neural Continuous-Discrete State Space Models for Irregularly-Sampled Time Seriescited by 28
  27. 2021Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Boundscited by 26
  28. 2023Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputationcited by 26
  29. 2023Bayesian Neural Controlled Differential Equations for Treatment Effect Estimationcited by 26
  30. 2022Interpretable Polynomial Neural Ordinary Differential Equationscited by 24
  31. 2022Predicting the impact of treatments over time with uncertainty aware neural differential equationscited by 23
  32. 2024Learning diffusion at lightspeedcited by 21
  33. 2021Differentiable Multiple Shooting Layerscited by 20
  34. 2023Defending against Adversarial Audio via Diffusion Modelcited by 20
  35. 2024Functional Bilevel Optimization for Machine Learningcited by 20
  36. 2025Comprehensive Review of Neural Differential Equations for Time Series Analysiscited by 20
  37. 2021Learning the temporal evolution of multivariate densities via normalizing flowscited by 18
  38. 2022TIDE: Time Derivative Diffusion for Deep Learning on Graphscited by 17

50 most cited of 264 All 264 (JSON)