mlsanityData to 7 Oct 2026

Stochastic Interpolants in Hilbert Spaces

arXiv 2602.01988 ↗First posted 2 Feb 2026stat.ML cs.LGcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Although diffusion models have successfully extended to function-valued data, stochastic interpolants -- which offer a flexible way to bridge arbitrary distributions -- remain limited to finite-dimensional settings. This work bridges this gap by establishing a rigorous framework for stochastic interpolants in infinite-dimensional Hilbert spaces. We provide comprehensive theoretical foundations, including proofs of well-posedness and explicit error bounds. We demonstrate the effectiveness of the proposed framework for conditional generation, focusing particularly on complex PDE-based benchmarks. By enabling generative bridges between arbitrary functional distributions, our approach achieves state-of-the-art results, offering a powerful, general-purpose tool for scientific discovery.

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 27 of its 58 references that are in the map. First posted on arXiv 2 Feb 2026.

Builds on

27 of 58 references.

Closest ancestors · 11

Same direction, newest first

  1. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spaces31 May
  2. 2024Conditioning non-linear and infinite-dimensional diffusion processes2 Feb
  3. 2023Infinite-Dimensional Diffusion Models20 Feb
  4. 2022Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions3 Nov
  5. 2022Spectral Diffusion Processes28 Sep
  6. 2022Convergence of denoising diffusion models under the manifold hypothesis10 Aug
  7. 2022Classifier-Free Diffusion Guidance26 Jul
  8. 2022Score-Based Generative Models Detect Manifolds2 Jun
  9. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  10. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  11. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 16

  1. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,550
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  3. 2022Imagen Video: High Definition Video Generation with Diffusion Modelscited by 1,765
  4. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 897
  5. 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
  6. 2022U-NO: U-shaped Neural Operatorscited by 219
  7. 2023Practical and Asymptotically Exact Conditional Sampling in Diffusion Modelscited by 218
  8. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observationcited by 100
  9. 2023Stochastic interpolants with data-dependent couplingscited by 94
  10. 2023Monte Carlo guided Diffusion for Bayesian linear inverse problemscited by 65
  11. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEscited by 33
  12. 2025Open Materials Generation with Stochastic Interpolantscited by 26
4 more
  1. 2024Basis-to-Basis Operator Learning Using Function Encoderscited by 17
  2. 2024Taming Score-Based Diffusion Priors for Infinite-Dimensional Nonlinear Inverse Problemscited by 7
  3. 2024Infinite-dimensional Diffusion Bridge Simulation via Operator Learningcited by 7
  4. 2025Autoregressive regularized score-based diffusion models for multi-scenarios fluid flow predictioncited by 2

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  1. 2022Diffusion Generative Models in Infinite Dimensions
  2. 2025On the Contractivity of Stochastic Interpolation Flow
  3. 2025Foundations of Diffusion Models in General State Spaces: A Self-Contained Introduction
  4. 2022An optimal control perspective on diffusion-based generative modeling
  5. 2024Non-asymptotic bounds for forward processes in denoising diffusions: Ornstein-Uhlenbeck is hard to beat
  6. 2024Reflected Schr"odinger Bridge for Constrained Generative Modeling
  7. 2023A Note on the Convergence of Denoising Diffusion Probabilistic Models
  8. 2026Infinite-dimensional generative diffusions via Doob's h-transform