mlsanityData to 7 Oct 2026

PhysDEM: Physics-Defined Energy-Matching Diffusion for Spatiotemporal Field Generation under Scarce Measurements

arXiv 2610.01759 ↗First posted 1 Oct 2026cs.CVcited by 0

On the map: Diffusion models → Flow matching, time series and science also fits: Diffusion foundations and sampling

Abstract (arXiv)

Generating and predicting spatiotemporal physical fields from scarce measurements is challenging, as observations are insufficient to characterize a distribution over complete fields. This limits conventional data-driven diffusion models that rely on full-field datasets. We introduce PhysDEM, a physics-defined diffusion framework that combines governing equations with spatially sparse observations to generate multiple plausible fields. First, we construct a Gibbs target by reweighting a measurement-conditioned Gaussian reference with PDE residual energy. Second, we derive an exact conditional-mean identity that reduces denoising to supervised learning of the standardized energy-induced mean correction. Third, a physics-displacement probability flow cancels Gaussian reference terms and enables amortized sampling with changing measurements through Gaussian conditioning, without retraining. Experiments on synthetic PDE systems and real-world-informed applications demonstrate that PhysDEM supports coherent field recovery and efficient sampling while maintaining stable diagnostics under tested noise levels, illustrating its practical value for field assessment. To our knowledge, PhysDEM is the first physics-defined diffusion model enabling amortized spatiotemporal field inference without preassembled full-field datasets.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in Flow matching, time series and science, one of 14 directions in Diffusion models. Builds on 21 of its 31 references that are in the map. First posted on arXiv 1 Oct 2026.

Builds on

21 of 31 references.

Closest ancestors · 6

Same direction, newest first

  1. 2026PHDME: Physics-Informed Diffusion Models without Explicit Governing Equations29 Jan
  2. 2025FunDiff: Diffusion Models over Function Spaces for Physics-Informed Generative Modeling9 Jun
  3. 2024DiffusionPDE: Generative PDE-Solving Under Partial Observation25 Jun
  4. 2024Physics-Informed Diffusion Models21 Mar
  5. 2023CoCoGen: Physically-Consistent and Conditioned Score-based Generative Models for Forward and Inverse Problems16 Dec
  6. 2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting3 Jun

Other references · 15

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  2. 2021Diffusion Models Beat GANs on Image Synthesiscited by 8,185
  3. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  4. 2021Skillful Precipitation Nowcasting using Deep Generative Models of Radarcited by 308
  5. 2024Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealingcited by 157
  6. 2023Denoising Diffusion Samplerscited by 144
  7. 2018Physics-Informed Generative Adversarial Networks for Stochastic Differential Equationscited by 133
  8. 2018Validating Bayesian Inference Algorithms with Simulation-Based Calibrationcited by 118
  9. 2024Iterated Denoising Energy Matching for Sampling from Boltzmann Densitiescited by 113
  10. 2024Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priorscited by 93
  11. 2023Score-based Data Assimilationcited by 91
  12. 2020Pathwise Conditioning of Gaussian Processescited by 63
3 more
  1. 2025Guided Diffusion Sampling on Function Spaces with Applications to PDEscited by 33
  2. 2025FNOPE: Simulation-based inference on function spaces with Fourier Neural Operatorscited by 3
  3. 2026Di-BiLPS: Denoising induced Bidirectional Latent-PDE-Solver under Sparse Observationscited by 1

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2025Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations
  2. 2026Multiphase-Diff: Diffusion-Based Generative Modeling for High-Contrast Multiphase Physical Systems with Sharp Interfaces
  3. 2024Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations
  4. 2026Learning Interpretable PDE Representations for Generative Reconstructions with Structured Sparsity
  5. 2026PILD: Physics-Informed Learning via Diffusion
  6. 2026PerFlow: Physics-Embedded Rectified Flow for Efficient Reconstruction and Uncertainty Quantification of Spatiotemporal Dynamics
  7. 2026Composing diffusion priors with explicit physical context via generative Gibbs sampling
  8. 2026Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fields