mlsanityData to 14 Oct 2026

Gaussian Interpolation Flows

arXiv 2311.11475 ↗First posted 20 Nov 2023stat.ML cs.LGcited by 17

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Abstract (arXiv)

Gaussian denoising has emerged as a powerful method for constructing simulation-free continuous normalizing flows for generative modeling. Despite their empirical successes, theoretical properties of these flows and the regularizing effect of Gaussian denoising have remained largely unexplored. In this work, we aim to address this gap by investigating the well-posedness of simulation-free continuous normalizing flows built on Gaussian denoising. Through a unified framework termed Gaussian interpolation flow, we establish the Lipschitz regularity of the flow velocity field, the existence and uniqueness of the flow, and the Lipschitz continuity of the flow map and the time-reversed flow map for several rich classes of target distributions. This analysis also sheds light on the auto-encoding and cycle consistency properties of Gaussian interpolation flows. Additionally, we study the stability of these flows in source distributions and perturbations of the velocity field, using the quadratic Wasserstein distance as a metric. Our findings offer valuable insights into the learning techniques employed in Gaussian interpolation flows for generative modeling, providing a solid theoretical foundation for end-to-end error analyses of learning Gaussian interpolation flows with empirical observations.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Builds on 60 of its 114 references that are in the map. First posted on arXiv 20 Nov 2023.

Builds on

60 of 114 references.

References · 60

  1. 2020Denoising Diffusion Probabilistic Modelscited by 21,076
  2. 2021High-Resolution Image Synthesis with Latent Diffusion Modelscited by 18,863
  3. 2020Denoising Diffusion Implicit Modelscited by 9,781
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  7. 2022Flow Matching for Generative Modelingcited by 5,702
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38 more
  1. 2022Elucidating the Design Space of Diffusion-Based Generative Modelscited by 3,045
  2. 2015Variational Inference with Normalizing Flowscited by 2,170
  3. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Stepscited by 1,979
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  7. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
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  9. 2022Building Normalizing Flows with Stochastic Interpolantscited by 995
  10. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  11. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 602
  12. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 594
  13. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusioncited by 459
  14. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptionscited by 445
  15. 2023Improved Techniques for Training Consistency Modelscited by 439
  16. 2023Multisample Flow Matching: Straightening Flows with Minibatch Couplingscited by 278
  17. 2023Flow Matching on General Geometriescited by 265
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 3; 2025: 9; 2026: 5.

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  1. 2024Convergence of Continuous Normalizing Flows for Learning Probability Distributionscited by 26
  2. 2025Lipschitz-Guided Design of Interpolation Schedules in Generative Modelscited by 17
  3. 2024Convergence Analysis of Flow Matching in Latent Space with Transformerscited by 16
  4. 2025Density Ratio Estimation with Conditional Probability Pathscited by 13
  5. 2026Flow Matching is Adaptive to Manifold Structurescited by 10
  6. 2025Error Analysis of Discrete Flow with Generator Matchingcited by 9
  7. 2025Mirror Flow Matching with Heavy-Tailed Priors for Generative Modeling on Convex Domainscited by 8
  8. 2025Distribution estimation via Flow Matching with Lipschitz guaranteescited by 6
  9. 2025Scale-Adaptive Generative Flows for Multiscale Scientific Datacited by 5
  10. 2025Elucidating Rectified Flow with Deterministic Sampler: Polynomial Discretization Complexity for Multi and One-step Modelscited by 3
  11. 2025On Conditional Stochastic Interpolation for Generative Nonlinear Sufficient Dimension Reductioncited by 3
  12. 2025From Conditional to Unconditional Independence: Testing Conditional Independence via Transport Mapscited by 2
5 more
  1. 2024New algorithms for sampling and diffusion modelscited by 1
  2. 2026Variational Optimality of F"ollmer Processes in Generative Diffusionscited by 1
  3. 2026Theoretical guidelines for annealed Langevin dynamics in compositional simulation-based inferencecited by 1
  4. 2026Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representationscited by 0
  5. 2026Flow Matching under Noisy Latent Structure: Beyond Exact Low-Dimensional Supportcited by 0