mlsanityData to 7 Oct 2026

Infinite-dimensional generative diffusions via Doob's h-transform

arXiv 2602.06621 ↗First posted 6 Feb 2026stat.ML cs.LGcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

This paper introduces a rigorous framework for defining generative diffusion models in infinite dimensions via Doob's h-transform. Rather than relying on time reversal of a noising process, a reference diffusion is forced towards the target distribution by an exponential change of measure. Compared to existing methodology, this approach readily generalises to the infinite-dimensional setting, hence offering greater flexibility in the diffusion model. The construction is derived rigorously under verifiable conditions, and bounds with respect to the target measure are established. We show that the forced process under the changed measure can be approximated by minimising a score-matching objective and validate our method on both synthetic and real data.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 38 of its 66 references that are in the map. First posted on arXiv 6 Feb 2026.

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38 of 66 references.

Closest ancestors · 18

Same direction, newest first

  1. 2025Beyond Fixed Horizons: A Theoretical Framework for Adaptive Denoising Diffusions31 Jan
  2. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spaces31 May
  3. 2024Conditioning non-linear and infinite-dimensional diffusion processes2 Feb
  4. 2023Non-Denoising Forward-Time Diffusions22 Dec
  5. 2023Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation8 Mar
  6. 2023Continuous-Time Functional Diffusion Processes1 Mar
  7. 2023Infinite-Dimensional Diffusion Models20 Feb
  8. 2023Score-based Diffusion Models in Function Space14 Feb
  9. 2022Diffusion Generative Models in Infinite Dimensions1 Dec
  10. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions22 Sep
  11. 2022Let us Build Bridges: Understanding and Extending Diffusion Generative Models31 Aug
  12. 2022How Much is Enough? A Study on Diffusion Times in Score-based Generative Models10 Jun
6 more
  1. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  2. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling1 Jun
  3. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  4. 2021Improved Denoising Diffusion Probabilistic Models18 Feb
  5. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  6. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 20

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2022Video Diffusion Modelscited by 2,280
  3. 2022Make-A-Video: Text-to-Video Generation without Text-Video Datacited by 1,725
  4. 2021Alias-Free Generative Adversarial Networkscited by 1,181
  5. 2022Diffusion-LM Improves Controllable Text Generationcited by 1,006
  6. 2021The Intrinsic Dimension of Images and Its Impact on Learningcited by 307
  7. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  8. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
  9. 2020MetaSDF: Meta-learning Signed Distance Functionscited by 214
  10. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstructioncited by 150
  11. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 105
  12. 2021Generative Models as Distributions of Functionscited by 89
8 more
  1. 2020Mat'ern Gaussian processes on Riemannian manifoldscited by 82
  2. 2023Diffusion Bridge Mixture Transports, Schr"odinger Bridge Problems and Generative Modelingcited by 80
  3. 2021Simulating Diffusion Bridges with Score Matchingcited by 51
  4. 2022Generative Adversarial Neural Operatorscited by 51
  5. 2023Conditional score-based diffusion models for Bayesian inference in infinite dimensionscited by 37
  6. 2023A framework for conditional diffusion modelling with applications in motif scaffolding for protein designcited by 22
  7. 2025h-Edit: Effective and Flexible Diffusion-Based Editing via Doob's h-Transformcited by 18
  8. 2024Infinite-dimensional Diffusion Bridge Simulation via Operator Learningcited by 7

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