Stable generative modelling using Schrödinger bridges

Area of Science:

• Computational Statistics
• Machine Learning
• Applied Mathematics

Background:

• Generative modeling and Bayesian inference increasingly rely on sampling from complex, unknown distributions.
• Existing methods face challenges with sample stability and computational efficiency.

Purpose of the Study:

• To propose a novel generative model combining Schrödinger bridges and Langevin dynamics for improved sample generation.
• To address stability issues in sampling from stiff stochastic differential equations.
• To extend the framework for conditional sampling and Bayesian inference.

Main Methods:

• Approximating conditional transition probabilities using Schrödinger bridges over a reversible reference process.
• Implementing a discrete-time reversible Langevin sampler.
• Utilizing a split-step scheme to maintain sample properties within the convex hull of training data.

Main Results:

• The proposed method effectively circumvents stability issues associated with time-stepping stiff stochastic differential equations.
• Generated samples are guaranteed to remain within the convex hull of the training samples.
• Demonstrated performance on synthetic data, subgrid-scale parametrization, and dynamical system trajectory generation.

Conclusions:

• The combined Schrödinger bridges and Langevin dynamics approach offers a stable and effective method for generative modeling and Bayesian inference.
• The framework's flexibility allows for extensions to conditional sampling and complex inverse problems.
• This work contributes to the synergy between generative modeling and Bayesian inference for inverse problems.