Approximate stochastic localization plus conductance transfers yield a weak Poincaré inequality for the SK model at β < 1/2, enabling efficient Glauber sampling from a warm start.
Nearly d-linear convergence bounds for diffu- sion models via stochastic localization.arXiv preprint arXiv:2308.03686
14 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Denoising diffusions are a powerful method to generate approximate samples from high-dimensional data distributions. Recent results provide polynomial bounds on their convergence rate, assuming $L^2$-accurate scores. Until now, the tightest bounds were either superlinear in the data dimension or required strong smoothness assumptions. We provide the first convergence bounds which are linear in the data dimension (up to logarithmic factors) assuming only finite second moments of the data distribution. We show that diffusion models require at most $\tilde O(\frac{d \log^2(1/\delta)}{\varepsilon^2})$ steps to approximate an arbitrary distribution on $\mathbb{R}^d$ corrupted with Gaussian noise of variance $\delta$ to within $\varepsilon^2$ in KL divergence. Our proof extends the Girsanov-based methods of previous works. We introduce a refined treatment of the error from discretizing the reverse SDE inspired by stochastic localization.
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A policy network learns to choose unmasking order in masked diffusion by reweighting the loss, outperforming random and heuristic baselines on ordering-sensitive tasks.
PGM framework links diffusion to proximal regularization for closed-form Moreau-score sampling in Bayesian inverse problems, learned only from prior samples.
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.
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.
For a broad class of coefficients, diffusion models achieve Õ(k/ε) iteration complexity for ε-accurate TV sampling under low-dimensional structure, independent of ambient dimension.
FM4PDE applies flow matching to learn joint PDE coefficient-solution distributions, using guided sampling with composite losses for forward and inverse problems and providing error guarantees under stated assumptions.
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.
HYVINT generates hypergraphs by learning latent Poisson interaction intensities and diffusing hyperedge-side variational embeddings, with asymptotic generation-error bounds and improved structural fidelity in its reported experiments.
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.
An educational exposition that layers core definitions, simplified estimates, and research-level theorems on diffusion sampling for probability-background graduate students.
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