First-order asymptotic expansions of weak and Fréchet discretization errors in diffusion sampling are derived, explicit under Gaussian data through covariance geometry and robust to other data geometries.
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P-Flow stabilizes flow-matching models for inverse problems via proxy gradients and Gaussian spherical projections, avoiding long-chain differentiation while maintaining prior consistency.
A preconditioned regularized Wasserstein proximal sampling algorithm is introduced for particle-based approximation of Gibbs distributions, featuring a PDE-derived kernel formulation and non-asymptotic convergence analysis for quadratic potentials.
UTOPY trains unrolling algorithms for ill-posed inverse problems via a fidelity homotopy path from synthetic well-posed to real ill-posed sensing operators, yielding up to 2.5 dB PSNR gains.
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Geometry-Aware Discretization Error of Diffusion Models
First-order asymptotic expansions of weak and Fréchet discretization errors in diffusion sampling are derived, explicit under Gaussian data through covariance geometry and robust to other data geometries.
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P-Flow: Proxy-gradient Flows for Linear Inverse Problems
P-Flow stabilizes flow-matching models for inverse problems via proxy gradients and Gaussian spherical projections, avoiding long-chain differentiation while maintaining prior consistency.