arXiv:2608.13383 2026 Sampling 1 ideas extracted · analyzed Sep 1, 2026
The paper develops a mixture-aware construction for transporting probability mass by augmenting continuous states with component labels and applying component-specific Markov kernels. This structure can become a generative sampler that preserves multimodality instead of forcing source and target mixtures through one global bridge. Its most actionable numerical contribution is covariance inflation, which trades a controlled O(epsilon^2) bias for improved conditioning and robustness to estimated covariances. A practical first test is a Gaussian-mixture Schrödinger bridge in a learned latent space, compared with a global diffusion bridge and direct mixture interpolation.
Represent both endpoint distributions as Gaussian mixtures and explicitly transport their component labels along with continuous states. Use an entropic coupling between source and target components, then run a separate Gaussian bridge for every selected component pair, with covariance inflation preventing unstable Riccati or Cholesky computations.