FHDMs achieve minimax optimal TV convergence rates for spherically supported Sobolev data distributions up to log factors, the first optimality result for random-time denoising diffusion models.
Aubin.Some nonlinear problems in Riemannian geometry
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A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.
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Statistical Convergence of Spherical First Hitting Diffusion Models
FHDMs achieve minimax optimal TV convergence rates for spherically supported Sobolev data distributions up to log factors, the first optimality result for random-time denoising diffusion models.
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On the Quantisation of Linear Gauge Theories on Lorentzian Manifolds: Maxwell's Theory via Complete Gauge Fixing
A new complete gauge fixing at initial data via Hodge decomposition on complete Riemannian manifolds enables existence proofs for Hadamard states in the quantization of Maxwell theory on globally hyperbolic Lorentzian manifolds.