A Unified Framework for Bayesian Data Assimilation with Generative Models and Observation Interpolants

arXiv:2610.03396 · cs.LG, cs.CE · Submitted 2026-10-02 · Read on arXiv

cs.LG, cs.CE

Submitted: 2026-10-02

Updated: 2026-10-02

Code: https://github.com/nmucke/scientific-stochastic-interpolants

Terminology

• Data Assimilation — 1× in this paper · explained in 2 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 3 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Building Normalizing Flows with Stochastic Interpolants
• Stochastic Interpolants: A Unifying Framework for Flows and Diffusions
• An Ensemble Score Filter for Tracking High-Dimensional Nonlinear Dynamical Systems
• D-Flow: Differentiating through Flows for Controlled Generation
• Data Assimilation in the Geosciences - An overview on methods, issues and perspectives
• FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation
• Probabilistic Forecasting with Stochastic Interpolants and F\"ollmer Processes
• Diffusion Posterior Sampling for General Noisy Inverse Problems
• A Survey on Diffusion Models for Inverse Problems
• Stochastic Flow Matching for Resolving Small-Scale Physics
• Denoising Diffusion Probabilistic Models
• Generator Matching: Generative modeling with arbitrary Markov processes
• Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation
• Flow Matching for Generative Modeling
• PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers
• Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow
• SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers
• PnP-Flow: Plug-and-Play Image Restoration with Flow Matching
• Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants
• D-Flow SGLD: Source-Space Posterior Sampling for Scientific Inverse Problems with Flow Matching

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