learnSDE

Code and notes of learning SDE from scratch

Theory

See Theory

Stochastic Neural Network

• On Neural Differential Equations
  [paper]
• Scalable Gradients for Stochastic Differential Equations
  [paper] [code]
• Efficient and Accurate Gradients for Neural SDEs
  [paper] [code]
• Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit
  [paper]
• Neural SDEs as Infinite-Dimensional GANs
  [paper] [code]

SPDE

• Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
  paper

• Neural Stochastic Partial Differential Equations
  paper

• Simulator-free Solution of High-dimensional Stochastic Elliptic Partial Differential Equations using Deep Neural Networks
  paper

• Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
  paper

• Deep Latent Regularity Network for Modeling Stochastic Partial Differential Equations
  paper

• Deep learning methods for stochastic Galerkin approximations of elliptic random PDEs
  paper

• Solving Stochastic Partial Differential Equations Using Neural Networks in the Wiener Chaos Expansion
  paper
  code

• Deep learning based numerical approximation algorithms for stochastic partial differential equations and high-dimensional nonlinear filtering problems
  paper

• A predictor-corrector deep learning algorithm for high dimensional stochastic partial differential equations
  paper

• Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
  paper

• Neural variational Data Assimilation with Uncertainty Quantification using SPDE priors
  paper

• Neural SPDE solver for uncertainty quantification in high-dimensional space-time dynamics
  paper

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SDE

• Neural SDE: Stabilizing Neural ODE Networks with Stochastic Noise 2019-2020CVPR paper

• SDE-Net: Equipping Deep Neural Networks with Uncertainty Estimates. ICML2020 [paper]

• Neural SDEs as Infinite-Dimensional GANs 2021ICML [paper] [code]

• Efficient and Accurate Gradients for Neural SDEs NIPS2021 [paper] [code]

• Learning stochastic dynamics with statistics-informed neural network JCP2023 paper

• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks 2023AAAI paper

• Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit
  paper

• Theoretical guarantees for sampling and inference in generative models with latent diffusions

• Neural Jump Stochastic Differential Equations

• Stochastic Normalizing Flows.

• Robust Pricing and Hedging via Neural SDEs.

• Scalable Gradients and Variational Inference for Stochastic Differential Equations.

Infinite Dimensional Diffusion

• Stochastic Equations in Infinite Dimensions (Book) 2014
  paper

• From Points to Functions: Infinite-Dimensional Representations in Diffusion Models 2022
  paper code

• Generative Models as Distributions of Functions AISTATS2022
  paper code

• Generative Modelling with Inverse Heat Dissipation 2023 ICLR2023
  paper code

• Infinite-Dimensional Diffusion Models 2023 JMLR2024
  paper

• Score-based Diffusion Models in Function Space 2023-2025
  paper code

• Diffusion Generative Models in Infinite Dimensions 2023 AISTATS2023
  paper code

• Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation 2023
  paper code

• Continuous-Time Functional Diffusion Processes NIPS2023
  paper

• \infty Diff: Infinite resolution diffusion with subsampled mollified states 2023 ICLR2024
  paper code

• Score-based Generative Modeling through Stochastic Evolution Equations in Hilbert Spaces NIPS2023
  paper

Infinite-dimensional Flow-based model

• Functional Flow Matching 2023
  paper code

• Conditioning non-linear and infinite-dimensional diffusion processes NIPS2024
  paper

• Stochastic Optimal Control for Diffusion Bridges in Function Spaces NIPS2024
  paper code

• Simulating Infinite-dimensional Nonlinear Diffusion Bridges 2024
  paper code

• Probability-Flow ODE in Infinite-Dimensional Function Spaces 2025
  paper

Generative Operator

• Generative Adversarial Neural Operators TMLR2022
  paper code

• Variational Autoencoding Neural Operators 2023 ICML paper

Diffusion PDE

• Generative PDE Control ICLR2024 workshop paper

• DiffPhyCon: A Generative Approach to Control Complex Physical Systems 2024 NIPS Oral paper

• DiffusionPDE: Generative PDE-Solving Under Partial Observation NIPS2024
  paper code

• Diffusion-Based Inverse Solver on Function Spaces With Applications to PDEs NIPS2024 workshop paper

• Guided Diffusion Sampling on Function Spaces with Applications to PDEs Maybe Underreview NIPS2025 paper

• FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling paper

• A Denoising Diffusion Model for Fluid Field Prediction paper

MultiPhysics

• M2PDE: Compositional Generative Multiphysics and Multi-component PDE Simulation ICLR 2025
  paper

• Neural ODE
• Efficient and Accurate Gradients for Neural SDEs