mlsanityData to 7 Oct 2026

User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systems

arXiv 2306.07526 ↗First posted 13 Jun 2023cs.LG cs.AIcited by 30

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Diffusion models are a class of probabilistic generative models that have been widely used as a prior for image processing tasks like text conditional generation and inpainting. We demonstrate that these models can be adapted to make predictions and provide uncertainty quantification for chaotic dynamical systems. In these applications, diffusion models can implicitly represent knowledge about outliers and extreme events; however, querying that knowledge through conditional sampling or measuring probabilities is surprisingly difficult. Existing methods for conditional sampling at inference time seek mainly to enforce the constraints, which is insufficient to match the statistics of the distribution or compute the probability of the chosen events. To achieve these ends, optimally one would use the conditional score function, but its computation is typically intractable. In this work, we develop a probabilistic approximation scheme for the conditional score function which provably converges to the true distribution as the noise level decreases. With this scheme we are able to sample conditionally on nonlinear userdefined events at inference time, and matches data statistics even when sampling from the tails of the distribution.

Key facts. Cited by 30 papers in the map (data through 7 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 22 of its 49 references that are in the map. First posted on arXiv 13 Jun 2023.

Builds on

22 of 49 references.

Closest ancestors · 5

Same direction, newest first

  1. 2022Diffusion models as plug-and-play priors17 Jun
  2. 2022Elucidating the Design Space of Diffusion-Based Generative Models1 Jun
  3. 2021Variational Diffusion Models1 Jul
  4. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
  5. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 17

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  3. 2022Photorealistic Text-to-Image Diffusion Models with Deep Language Understandingcited by 6,322
  4. 2022Generative Adversarial Networkscited by 5,603
  5. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  6. 2018Neural Ordinary Differential Equationscited by 3,733
  7. 2022RePaint: Inpainting using Denoising Diffusion Probabilistic Modelscited by 1,419
  8. 2022Diffusion Posterior Sampling for General Noisy Inverse Problemscited by 1,375
  9. 2018FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Modelscited by 584
  10. 2022Improving Diffusion Models for Inverse Problems using Manifold Constraintscited by 501
  11. 2021Score-based diffusion models for accelerated MRIcited by 308
  12. 2021Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contractioncited by 306
5 more
  1. 2019Residual Flows for Invertible Generative Modelingcited by 256
  2. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 102
  3. 2023A Theoretical Justification for Image Inpainting using Denoising Diffusion Probabilistic Modelscited by 37
  4. 2019Flood Prediction Using Machine Learning Models: Literature Reviewcited by 36
  5. 2021Model-assisted deep learning of rare extreme events from partial observationscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 13; 2025: 9; 2026: 6.

30 papers.

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  1. 2024Learning Diffusion Priors from Observations by Expectation Maximizationcited by 60
  2. 2024On conditional diffusion models for PDE simulationscited by 56
  3. 2024DEFT: Efficient Fine-Tuning of Diffusion Models by Learning the Generalised h-transformcited by 44
  4. 2024Variational Diffusion Posterior Sampling with Midpoint Guidancecited by 32
  5. 2024Divide-and-Conquer Posterior Sampling for Denoising Diffusion Priorscited by 28
  6. 2023A framework for conditional diffusion modelling with applications in motif scaffolding for protein designcited by 22
  7. 2024Adding Conditional Control to Diffusion Models with Reinforcement Learningcited by 16
  8. 2024Free Hunch: Denoiser Covariance Estimation for Diffusion Models Without Extra Costscited by 14
  9. 2026Improving Flow Matching by Aligning Flow Divergencecited by 9
  10. 2023Diffusion Methods for Generating Transition Pathscited by 8
  11. 2024Equivariant Denoisers Cannot Copy Graphs: Align Your Graph Diffusion Modelscited by 7
  12. 2025Efficient Zero-Shot Inpainting with Decoupled Diffusion Guidancecited by 5
18 more
  1. 2024A Comprehensive Survey on Diffusion Models and Their Applicationscited by 4
  2. 2024Back-Projection Diffusion: Solving the Wideband Inverse Scattering Problem with Diffusion Modelscited by 3
  3. 2025Generative Learning for Slow Manifolds and Bifurcation Diagramscited by 3
  4. 2025PriorGuide: Test-Time Prior Adaptation for Simulation-Based Inferencecited by 3
  5. 2026Supervised Guidance Training for Infinite-Dimensional Diffusion Modelscited by 3
  6. 2026RMFlow: Refined Mean Flow by a Noise-Injection Step for Multimodal Generationcited by 3
  7. 2025Score-Based Turbo Message Passing for Plug-and-Play Compressive Image Recoverycited by 2
  8. 2025Using Ensemble Diffusion to Estimate Uncertainty for End-to-End Autonomous Drivingcited by 2
  9. 2025Improved probabilistic regression using diffusion modelscited by 2
  10. 2025Latent Refinement via Flow Matching for Training-free Linear Inverse Problem Solvingcited by 2
  11. 2024Diffusing Differentiable Representationscited by 1
  12. 2025Discrete Spatial Diffusion: Intensity-Preserving Diffusion Modelingcited by 1
  13. 2026LatentFlow: A General Framework for Conditioning Stochastic Processescited by 1
  14. 2026Second Order Drifting Modelscited by 1
  15. 2024Diffusion-based subsurface CO2 multiphysics monitoring and forecastingcited by 0
  16. 2024Improving the Noise Estimation of Latent Neural Stochastic Differential Equationscited by 0
  17. 2025Briding Diffusion Posterior Sampling and Monte Carlo methods: a surveycited by 0
  18. 2026Target-Aware Linear Regression Under Distribution Shiftcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025Generative Uncertainty in Diffusion Models
  2. 2024Conditional sampling within generative diffusion models
  3. 2024Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory
  4. 2025Information-Theoretic Proofs for Diffusion Sampling
  5. 2026A Plug-in Interpretation of Conditioning in Score-Based Diffusion Models
  6. 2025Predicting partially observable dynamical systems via diffusion models with a multiscale inference scheme
  7. 2024Shedding Light on Large Generative Networks: Estimating Epistemic Uncertainty in Diffusion Models
  8. 2026A Tutorial on Diffusion Theory: From Differential Equations to Diffusion Models