Transport with Support: Data-Conditional Diffusion Bridges
This work addresses constrained time-series data generation for applications like modeling biological sequences or sampling from complex posteriors, representing an incremental improvement over prior methods.
The paper tackles the limitation of existing dynamic Schrödinger bridge methods, which only handle initial and terminal constraints, by proposing the Iterative Smoothing Bridge (ISB) to incorporate sparse intermediate observations, showing it generalizes well to high-dimensional data, is computationally efficient, and provides accurate marginal estimates.
The dynamic Schrödinger bridge problem provides an appealing setting for solving constrained time-series data generation tasks posed as optimal transport problems. It consists of learning non-linear diffusion processes using efficient iterative solvers. Recent works have demonstrated state-of-the-art results (eg. in modelling single-cell embryo RNA sequences or sampling from complex posteriors) but are limited to learning bridges with only initial and terminal constraints. Our work extends this paradigm by proposing the Iterative Smoothing Bridge (ISB). We integrate Bayesian filtering and optimal control into learning the diffusion process, enabling the generation of constrained stochastic processes governed by sparse observations at intermediate stages and terminal constraints. We assess the effectiveness of our method on synthetic and real-world data generation tasks and we show that the ISB generalises well to high-dimensional data, is computationally efficient, and provides accurate estimates of the marginals at intermediate and terminal times.