Adapting Noise to Data: Generative Flows from 1D Processes
Not on the map. Why?
Abstract (arXiv)
The default Gaussian latent in flow-based generative models poses challenges when learning certain distributions such as heavy-tailed ones. We introduce a general framework for learning data-adaptive parametric prior distributions (latent noise) using one-dimensional quantile functions, optimized via the Wasserstein distance between noise and data. The quantile-based prior parameterization naturally adapts to both heavy-tailed and compactly supported distributions and shortens transport paths. Numerical results on heavy-tailed weather and image datasets confirm the method's flexibility and effectiveness achieved with negligible computational overhead.
Key facts. No citing papers in the map yet (data through 13 Oct 2026). Builds on 39 of its 60 references that are in the map. First posted on arXiv 14 Oct 2025.
Builds on
39 of 60 references.
References · 39
- 2020Denoising Diffusion Probabilistic Modelscited by 20,952
- 2020Denoising Diffusion Implicit Modelscited by 9,718
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,028
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,023
- 2022Flow Matching for Generative Modelingcited by 5,542
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,077
- 2021Improved Denoising Diffusion Probabilistic Modelscited by 3,751
- 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,607
- 2023Consistency Modelscited by 1,797
- 2021Structured Denoising Diffusion Models in Discrete State-Spacescited by 1,685
- 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 917
- 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 857
27 more
- 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 672
- 2019Neural Spline Flowscited by 590
- 2025Mean Flows for One-step Generative Modelingcited by 541
- 2024Flow Matching Guide and Codecited by 295
- 2022Rectified Flow: A Marginal Preserving Approach to Optimal Transportcited by 281
- 2022Score-Based Generative Models Detect Manifoldscited by 122
- 2025Inductive Moment Matchingcited by 110
- 2025How to build a consistency model: Learning flow maps via self-distillationcited by 101
- 2021Soft Truncation: A Universal Training Technique of Score-based Diffusion Model for High Precision Score Estimationcited by 95
- 2024Metric Flow Matching for Smooth Interpolations on the Data Manifoldcited by 76
- 2018Resampled Priors for Variational Autoencoderscited by 56
- 2023Diffusion Models With Learned Adaptive Noisecited by 51
- 2024Neural Flow Diffusion Models: Learnable Forward Process for Improved Diffusion Modellingcited by 45
- 2021Resampling Base Distributions of Normalizing Flowscited by 42
- 2022Can Push-forward Generative Models Fit Multimodal Distributions?cited by 41
- 2024Heavy-Tailed Diffusion Modelscited by 35
- 2020Stabilizing Invertible Neural Networks Using Mixture Modelscited by 30
- 2025Underdamped Diffusion Bridges with Applications to Samplingcited by 28
- 2019Copula & Marginal Flows: Disentangling the Marginal from its Jointcited by 17
- 2025Flow Matching: Markov Kernels, Stochastic Processes and Transport Planscited by 17
- 2022Wasserstein Steepest Descent Flows of Discrepancies with Riesz Kernelscited by 16
- 2024Heavy-Tailed Diffusion with Denoising L'evy Probabilistic Modelscited by 16
- 2024Flexible Tails for Normalizing Flowscited by 11
- 2025Designing a Conditional Prior Distribution for Flow-Based Generative Modelscited by 9
- 2024Wasserstein Gradient Flows of MMD Functionals with Distance Kernel and Cauchy Problems on Quantile Functionscited by 7
- 2025Telegrapher's Generative Model via Kac Flowscited by 7
- 2025On the Statistical Capacity of Deep Generative Modelscited by 2
Built on by
Not cited yet.