Chromatic Gibbs Sampling for Long-Range Data Assimilation

Estimating the state of an evolving system from intermittent, noisy observations is a central scientific problem, known as data assimilation (DA). Training generative models directly for long-range DA, such as atmosphere or ocean state estimation, can be prohibitively expensive. A common alternative is to compose models with short time horizons at inference. However, existing composition methods fail to sample from the target assimilation distribution, either due to approximations or intrinsic flaws. Drawing from the Gibbs sampling and graphical model literature, we introduce GiBBS, an iterative method for composing Markov-local generative models that provably converges to the target distribution under reasonable assumptions. We validate and ablate our method on the classical Ornstein-Uhlenbeck and Lorenz-63 systems, before scaling it to high-dimensional Kuramoto-Sivashinsky and turbulent Navier-Stokes systems. Across these experiments, GiBBS consistently and substantially improves upon its initial guess in few (1-16) cycles, highlighting its potential for operational assimilation.