Lifted Schrödinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructions
We study stochastic density control between Gaussian-mixture endpoint distributions under Brownian prior dynamics. Since the direct Schrödinger bridge between Gaussian mixtures is generally not available in closed form, we introduce a lifted path-space construction in which each trajectory is augmented with a source--target component label. Consequently, the problem decomposes into Gaussian component-to-component Schrödinger bridges with explicit marginal, drift, and cost formulas, while the mixture-level assignment reduces to a finite-dimensional entropic coupling problem with a Sinkhorn scaling form. We then analyze the projection obtained by discarding or forgetting the label. By const...
| Authors | Siddhartha Ganguly, George Rapakoulias, Panagiotis Tsiotras |
|---|---|
| Primary category | math.OC |
| Published | 24 May 2026 |
| Last updated at source | 12 June 2026 |
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