MM-SOLD is a training-free particle sampler whose large-particle limit converges to a moment-matched Gibbs distribution obtained by exponentially tilting a score-smoothed target.
Score-based generative models detect manifolds.Advances in Neural Information Processing Systems, 35:35852–35865, 2022
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Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
Empirical flow matching introduces coupled biases from plug-in estimation, including altered statistical targets, non-gradient minimizers, and non-unique dynamics via flux-null fields, with base distribution controlling kinetic energy tails.
SiLD is a score-matching framework that learns both manifold projection and intrinsic density from a single objective, with proven sample complexity depending only on intrinsic dimension.
citing papers explorer
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Training-Free Generative Sampling via Moment-Matched Score Smoothing
MM-SOLD is a training-free particle sampler whose large-particle limit converges to a moment-matched Gibbs distribution obtained by exponentially tilting a score-smoothed target.
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Diffusion Processes on Implicit Manifolds
Defines diffusion processes on implicit data manifolds via proximity-graph approximations to the infinitesimal generator and carré-du-champ operator, proves convergence in law to the continuous manifold process, and provides an Euler-Maruyama integrator validated on synthetic and MNIST manifolds.
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On The Hidden Biases of Flow Matching Samplers
Empirical flow matching introduces coupled biases from plug-in estimation, including altered statistical targets, non-gradient minimizers, and non-unique dynamics via flux-null fields, with base distribution controlling kinetic energy tails.
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Provably Learning Diffusion Models under the Manifold Hypothesis: Collapse and Refine
SiLD is a score-matching framework that learns both manifold projection and intrinsic density from a single objective, with proven sample complexity depending only on intrinsic dimension.