Provides a posterior-transport analysis of flow-based inverse solvers, demonstrating that source reweighting yields exact posteriors while trajectory guidance methods are zeroth-order/Gaussian/proximal approximations incurring Wasserstein bias, and proposes a competitive velocity-correction solver.
Monte carlo guided denoising diffusion models for bayesian linear inverse problems
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What Do Flow-Based Inverse Solvers Approximate? A Posterior-Transport View
Provides a posterior-transport analysis of flow-based inverse solvers, demonstrating that source reweighting yields exact posteriors while trajectory guidance methods are zeroth-order/Gaussian/proximal approximations incurring Wasserstein bias, and proposes a competitive velocity-correction solver.