mlsanityData to 14 Oct 2026

Variational Gaussian Process Diffusion Processes

arXiv 2306.02066 ↗First posted 3 Jun 2023cs.LG stat.MLcited by 11

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Abstract (arXiv)

Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with latent processes endowed with a non-linear diffusion process prior are intractable problems. We build upon work within variational inference, approximating the posterior process as a linear diffusion process, and point out pathologies in the approach. We propose an alternative parameterization of the Gaussian variational process using a site-based exponential family description. This allows us to trade a slow inference algorithm with fixed-point iterations for a fast algorithm for convex optimization akin to natural gradient descent, which also provides a better objective for learning model parameters.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 28 of its 68 references that are in the map. First posted on arXiv 3 Jun 2023.

Builds on

28 of 68 references.

References · 28

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,255
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2016Variational Inference: A Review for Statisticianscited by 1,472
  5. 2022Planning with Diffusion for Flexible Behavior Synthesiscited by 1,061
  6. 2021Maximum Likelihood Training of Score-Based Diffusion Modelscited by 672
  7. 2021CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputationcited by 582
  8. 2020Scalable Gradients for Stochastic Differential Equationscited by 271
  9. 2013Expectation Propagation for approximate Bayesian inferencecited by 174
  10. 2021Solving Schr"odinger Bridges via Maximum Likelihoodcited by 141
  11. 2021Efficient and Accurate Gradients for Neural SDEscited by 71
  12. 2017Conjugate-Computation Variational Inference : Converting Variational Inference in Non-Conjugate Models to Inferences in Conjugate Modelscited by 65
16 more
  1. 2019Fast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-family Approximationscited by 51
  2. 2018Fast yet Simple Natural-Gradient Descent for Variational Inference in Complex Modelscited by 38
  3. 2019Learning interpretable continuous-time models of latent stochastic dynamical systemscited by 30
  4. 2018Black-box Variational Inference for Stochastic Differential Equationscited by 25
  5. 2018Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matchingcited by 23
  6. 2014Particle Gibbs with Ancestor Samplingcited by 21
  7. 2020Fast Variational Learning in State-Space Gaussian Process Modelscited by 20
  8. 2021Dual Parameterization of Sparse Variational Gaussian Processescited by 19
  9. 2021Bayes-Newton Methods for Approximate Bayesian Inference with PSD Guaranteescited by 13
  10. 2017Non-parametric Estimation of Stochastic Differential Equations with Sparse Gaussian Processescited by 12
  11. 2021Sparse Algorithms for Markovian Gaussian Processescited by 10
  12. 2021Variational Inference for Continuous-Time Switching Dynamical Systemscited by 10
  13. 2021Moment-Based Variational Inference for Stochastic Differential Equationscited by 6
  14. 2015Expectation propagation for continuous time stochastic processescited by 4
  15. 2015Nonlinear state space smoothing using the conditional particle filtercited by 3
  16. 2018Gaussian process classification using posterior linearisationcited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 6; 2026: 2.

11 papers.

  1. 2023On the Design Fundamentals of Diffusion Models: A Surveycited by 60
  2. 2025SDE Matching: Scalable and Simulation-Free Training of Latent Stochastic Differential Equationscited by 23
  3. 2024Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systemscited by 11
  4. 2025In-Context Learning of Stochastic Differential Equations with Foundation Inference Modelscited by 7
  5. 2025SING: SDE Inference via Natural Gradientscited by 5
  6. 2025Topological Schr"odinger Bridge Matchingcited by 4
  7. 2026Foundation Inference Models for Ordinary Differential Equationscited by 3
  8. 2025Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Modelscited by 1
  9. 2024Learning to Approximate Particle Smoothing Trajectories via Diffusion Generative Modelscited by 0
  10. 2025Recursive Entropic Variational Inference for Nonlinear State-Space Modelscited by 0
  11. 2026Gaussian Flow Dynamics: Simulation-Free Neural SDE Learning Beyond One-Time Marginalscited by 0