Predict-Project-Renoise: Sampling Diffusion Models under Hard Constraints
On the map: Diffusion models → Diffusion foundations and sampling
Abstract (arXiv)
Diffusion models cannot enforce hard constraints, yet applications in the physical sciences demand exact satisfaction of conservation laws, boundary conditions, and observational consistency. In this work, we identify a corrector kernel whose unique stationary distribution is the constrained marginal at each noise level, and approximate it by iteratively projecting through the denoiser and renoising via the forward kernel. The resulting Predict-Project-Renoise (PPR) algorithm enables sampling from pretrained diffusion models under hard constraints. Its three components are each necessary: projecting through the denoiser keeps samples close to the data manifold, while renoising and iterating drive samples toward the constrained marginal. On 2D distributions, the Kuramoto-Sivashinsky equation, and global weather forecasting with a 108-dimensional atmospheric model, PPR simultaneously achieves low constraint violations and high distributional fidelity, a combination that existing methods fail to deliver.
Key facts. Cited by 2 papers in the map (data through 13 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 18 of its 40 references that are in the map. First posted on arXiv 28 Jan 2026.
Builds on
18 of 40 references.
Closest ancestors · 7
Same direction, newest first
- 2025Learn to Guide Your Diffusion Model1 Oct
- 2025Constrained Generative Modeling with Manually Bridged Diffusion Models27 Feb
- 2024Constrained Synthesis with Projected Diffusion Models5 Feb
- 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
- 2021Diffusion Models Beat GANs on Image Synthesis11 May
- 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
- 2020Denoising Diffusion Probabilistic Models19 Jun
Other references · 11
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,023
- 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,403
- 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 508
- 2023Solving Inverse Problems with Latent Diffusion Models via Hard Data Consistencycited by 181
- 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 61
- 2025Training-Free Constrained Generation With Stable Diffusion Modelscited by 20
- 2023L-C2ST: Local Diagnostics for Posterior Approximations in Simulation-Based Inferencecited by 17
- 2024Generating Physical Dynamics under Priorscited by 6
- 2024Constrained Posterior Sampling: Time Series Generation with Hard Constraintscited by 6
- 2025Constrained Diffusion for Protein Design with Hard Structural Constraintscited by 5
- 2025Enforcing governing equation constraints in neural PDE solvers via training-free projectionscited by 4
Built on by
Citing papers per year: 2026: 2.
2 papers.
Similar, not cited
Close in wording, no citation either way
- 2023Metropolis Sampling for Constrained Diffusion Models
- 2025Softly Constrained Denoisers for Diffusion Models Applied to Partial Differential Equations
- 2026Universal Diffusion-Based Probabilistic Downscaling
- 2026When Denoising Hurts: Rethinking the Terminal Step of Diffusion Time Series Forecasters -- Extended Version
- 2025Predictive posterior sampling from non-stationnary Gaussian process priors via Diffusion models with application to climate data
- 2023Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models
- 2024DiffDA: a Diffusion Model for Weather-scale Data Assimilation
- 2024Fast constrained sampling in pre-trained diffusion models