mlsanityData to 7 Oct 2026

Score-based constrained generative modeling via Langevin diffusions with boundary conditions

arXiv 2510.23985 ↗First posted 28 Oct 2025stat.ML cs.LG cs.NAcited by 2

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Score-based generative models based on stochastic differential equations (SDEs) achieve impressive performance in sampling from unknown distributions, but often fail to satisfy underlying constraints. We propose a constrained generative model using kinetic (underdamped) Langevin dynamics with specular reflection of velocity on the boundary defining constraints. This results in piecewise continuously differentiable noising and denoising process where the latter is characterized by a time-reversed dynamics restricted to a domain with boundary due to specular boundary condition. In addition, we also contribute to existing reflected SDEs based constrained generative models, where the stochastic dynamics is restricted through an abstract local time term. By presenting efficient numerical samplers which converge with optimal rate in terms of discretizations step, we provide a comprehensive comparison of models based on confined (specularly reflected kinetic) Langevin diffusion with models based on reflected diffusion with local time.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 12 of its 43 references that are in the map. First posted on arXiv 28 Oct 2025.

Builds on

12 of 43 references.

Closest ancestors · 8

Same direction, newest first

  1. 2025Constrained Generative Modeling with Manually Bridged Diffusion Models27 Feb
  2. 2024Constrained Diffusion Models via Dual Training27 Aug
  3. 2024Constrained Synthesis with Projected Diffusion Models5 Feb
  4. 2024Reflected Schr"odinger Bridge for Constrained Generative Modeling6 Jan
  5. 2023Metropolis Sampling for Constrained Diffusion Models11 Jul
  6. 2021Score-Based Generative Modeling with Critically-Damped Langevin Diffusion14 Dec
  7. 2021Diffusion Models Beat GANs on Image Synthesis11 May
  8. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov

Other references · 4

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  3. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  4. 2023Sampling and estimation on manifolds using the Langevin diffusioncited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Picasso: Holistic Scene Reconstruction with Physics-Constrained Samplingcited by 4
  2. 2026Should the Boundary Term Be Learned in Reflected Diffusion? Conormal Trace and Reflection Maskingcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Generative Modelling with High-Order Langevin Dynamics
  2. 2022Sampling is as easy as learning the score: theory for diffusion models with minimal data assumptions
  3. 2024Discrete vs. Continuous Trade-offs for Generative Models
  4. 2022A Flexible Diffusion Model
  5. 2025Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling
  6. 2026Gradient-Free Sampling from Generative Models via Stochastic Bounded Extremum Seeking
  7. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models
  8. 2023Reflected Diffusion Models