Consistency Training with Physical Constraints
On the map: Diffusion models → Flow matching, time series and science
Abstract (arXiv)
We propose a physics-aware Consistency Training (CT) method that accelerates sampling in Diffusion Models with physical constraints. Our approach leverages a two-stage strategy: (1) learning the noise-to-data mapping via CT, and (2) incorporating physics constraints as a regularizer. Experiments on toy examples show that our method generates samples in a single step while adhering to the imposed constraints. This approach has the potential to efficiently solve partial differential equations (PDEs) using deep generative modeling.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 9 of its 11 references that are in the map. First posted on arXiv 11 Feb 2025.
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9 of 11 references.
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- 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction26 Nov
- 2022Diffusion Models Beat GANs on Topology Optimization20 Aug
Other references · 7
- 2020Denoising Diffusion Probabilistic Modelscited by 21,076
- 2020Denoising Diffusion Implicit Modelscited by 9,781
- 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
- 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
- 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
- 2023Consistency Modelscited by 1,822
- 2023Improved Techniques for Training Consistency Modelscited by 439
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- 2026Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training
- 2025Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation
- 2024Truncated Consistency Models
- 2024Physics-Informed Diffusion Models
- 2026Source Anchoring for Physical Consistency in Flow Matching Models
- 2024Improving Consistency Models with Generator-Augmented Flows
- 2026PILD: Physics-Informed Learning via Diffusion
- 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraints