# Conditional Denoising Model as a Physical Surrogate Model

arXiv: https://arxiv.org/abs/2601.21021 · HTML: https://mlsanity.com/paper/2601.21021/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 43 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [PhysDiff: Physics-Guided Human Motion Diffusion Model](https://mlsanity.com/paper/2212.02500/) (2022)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Learning Energy-Based Models by Diffusion Recovery Likelihood](https://mlsanity.com/paper/2012.08125/) (2020)
- [Generalized Denoising Auto-Encoders as Generative Models](https://mlsanity.com/paper/1305.6663/) (2013)
- [CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems](https://mlsanity.com/paper/2312.10527/) (2023)
- [Equilibrium Matching: Generative Modeling with Implicit Energy-Based Models](https://mlsanity.com/paper/2510.02300/) (2025)
- [Diffusion Models for Molecules: A Survey of Methods and Tasks](https://mlsanity.com/paper/2502.09511/) (2025)
- [Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion model](https://mlsanity.com/paper/2310.01678/) (2023)
- [Training Energy-Based Models with Diffusion Contrastive Divergences](https://mlsanity.com/paper/2307.01668/) (2023)
- [Random Walks with Tweedie: A Unified View of Score-Based Diffusion Models](https://mlsanity.com/paper/2411.18702/) (2024)
- [Physics-consistent machine learning: output projection onto physical manifolds](https://mlsanity.com/paper/2502.15755/) (2025)
- [A Score-based Generative Solver for PDE-constrained Inverse Problems with Complex Priors](https://mlsanity.com/paper/2408.16626/) (2024)
- [Integration Matters for Learning PDEs with Backward SDEs](https://mlsanity.com/paper/2505.01078/) (2025)

## Abstract (arXiv)

Surrogate modeling for complex physical systems typically faces a trade-off between data-fitting accuracy and physical consistency. Physics-consistent approaches typically treat physical laws as soft constraints within the loss function, a strategy that frequently fails to guarantee strict adherence to the governing equations, or rely on post-processing corrections that do not intrinsically learn the underlying solution geometry. To address these limitations, we introduce the {Conditional Denoising Model (CDM)}, a generative model designed to learn the geometry of the physical manifold itself. By training the network to restore clean states from noisy ones, the model learns a vector field that points continuously towards the valid solution subspace. We introduce a time-independent formulation that transforms inference into a deterministic fixed-point iteration, effectively projecting noisy approximations onto the equilibrium manifold. Validated on a low-temperature plasma physics and chemistry benchmark, the CDM achieves higher parameter and data efficiency than physics-consistent baselines. Crucially, we demonstrate that the denoising objective acts as a powerful implicit regularizer: despite never seeing the governing equations during training, the model adheres to physical constraints more strictly than baselines trained with explicit physics losses.