Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
Nearlyd-linear convergence bounds for diffusion models via stochastic local- ization.CoRR, abs/2308.03686
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Discrete Stochastic Localization lets a single trained network support an entire family of per-token SNR paths for discrete sequence generation, with masked diffusion as a special case, and improves MAUVE scores when fine-tuning pretrained checkpoints.
SCSI iteratively refines a self-consistent transport map to invert black-box corruptions and enable generative modeling of clean data.
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.
Training and sampling in static scalar energy generative models are two instances of the same Lyapunov-driven density transport dynamics on Wasserstein space, differing only by initial condition, which yields a finite stopping criterion for Langevin sampling and additive composition rules that keep
A plug-in estimator for tilted distributions is minimax-optimal, with Wasserstein closeness bounds to the true tilted distribution and TV-accuracy guarantees when running diffusion on the estimated samples.
Diffusion models on manifold-supported data admit score decompositions whose statistical rates are controlled by intrinsic dimension and curvature.
HYVINT introduces an intensity-driven incidence mechanism and tractable variational estimator for hypergraph generation, with error bounds and empirical gains in fidelity, novelty, and diversity.
citing papers explorer
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Potential Hessian Ascent III: Sampling the Sherrington--Kirkpatrick Model at Beta < 1/2
Polynomial-time algorithm samples the Sherrington-Kirkpatrick Gibbs measure at beta < 1/2 with o(1) TVD error by combining potential Hessian ascent, stochastic localization, covariance estimates, and Jarzynski equality with rejection sampling.
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Discrete Stochastic Localization for Non-autoregressive Generation
Discrete Stochastic Localization lets a single trained network support an entire family of per-token SNR paths for discrete sequence generation, with masked diffusion as a special case, and improves MAUVE scores when fine-tuning pretrained checkpoints.
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Generative Modeling from Black-box Corruptions via Self-Consistent Stochastic Interpolants
SCSI iteratively refines a self-consistent transport map to invert black-box corruptions and enable generative modeling of clean data.
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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.
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Energy Generative Modeling: A Lyapunov-based Energy Matching Perspective
Training and sampling in static scalar energy generative models are two instances of the same Lyapunov-driven density transport dynamics on Wasserstein space, differing only by initial condition, which yields a finite stopping criterion for Langevin sampling and additive composition rules that keep
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Generating DDPM-based Samples from Tilted Distributions
A plug-in estimator for tilted distributions is minimax-optimal, with Wasserstein closeness bounds to the true tilted distribution and TV-accuracy guarantees when running diffusion on the estimated samples.
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Diffusion Model for Manifold Data: Score Decomposition, Curvature, and Statistical Complexity
Diffusion models on manifold-supported data admit score decompositions whose statistical rates are controlled by intrinsic dimension and curvature.
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HYVINT: Intensity-Driven Hypergraph Generation with Variational Representations
HYVINT introduces an intensity-driven incidence mechanism and tractable variational estimator for hypergraph generation, with error bounds and empirical gains in fidelity, novelty, and diversity.
- Proximal-Based Generative Modeling for Bayesian Inverse Problems