arXiv research

The paper studies a 1D diffusion equation with nonlinear Robin boundary conditions and finds conditions for global and finite time blow-up or blow-down.

Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get functional inequalities as Poincaré or logarithmic Sobolev inequalities. Moreover an alternative method using the optimal mass transportation, is also given to obtain the logarithmic Sobolev inequa…

Study of diffusion annealed Langevin dynamics for generative models.

First, classes of Markov processes that scale exactly with a Hurst exponent H are derived in closed form. A special case of one class is the Tsallis density, advertised elsewhere as nonlinear diffusion or diffusion with nonlinear feedback. But the Tsallis model is only one of a very large class of linear diffusion with…

Uniform heat kernel and diffusion bridge asymptotics for sub-Riemannian geometry.

We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the case of the Gaussian logarithmic returns model by Harrison and Kreps, but we prove …

This work improves the convergence theory of diffusion models for generating samples from complex distributions.

Study bounds for Brownian motion on manifolds with sticky boundary conditions.

New diffusion models handle constrained domains, improving generative tasks.

A new algorithm solves semidefinite programs using Langevin diffusion.

We prove the sharp local L^1 - L^\infty smoothing estimate for the logarithmic fast diffusion equation, or equivalently, for the Ricci flow on surfaces. Our estimate almost instantly implies an improvement of the known L^p - L^\infty estimate for p larger than 1. It also has several applications in geometry, providing …

Paper optimizes approximating high-dimensional diffusions by independent coordinates.

Study on policy gradient for stochastic bandits using diffusion approximation.

High-dimensional curved diffusions show abrupt convergence at a critical time.

New bounds close the score matching gap for diffusion models.

Unified framework for denoising models across various spaces.

Diffusion models converge linearly to complex data manifolds.

New bounds show diffusion models converge nearly linearly in data dimension.

Diffusion models achieve high-quality samples from complex high-dimensional Gaussian mixtures without scaling with dimension.

Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.

Flow Matching improves statistical guarantees through kernel density estimation.

Sharp 2-Wasserstein bounds for DDPMs derived from Föllmer process.

FHDMs achieve optimal convergence in spherically supported data.

Entropy tracking reveals class commitment transitions in diffusion models.

A stock market is called diverse if no stock can dominate the market in terms of relative capitalization. On one hand, this natural property leads to arbitrage in diffusion models under mild assumptions. On the other hand, it is also easy to construct diffusion models which are both diverse and free of arbitrage. Can o…

Affine jump-diffusions constitute a large class of continuous-time stochastic models that are particularly popular in finance and economics due to their analytical tractability. Methods for parameter estimation for such processes require ergodicity in order establish consistency and asymptotic normality of the associat…

For incomplete sub-Riemannian manifolds, and for an associated second-order hypoelliptic operator, which need not be symmetric, we identify two alternative conditions for the validity of Gaussian-type upper bounds on heat kernels and transition probabilities, with optimal constant in the exponent. Under similar conditi…

New theory improves diffusion model convergence for generating data.

Improved image generation quality using closed-form discriminator guidance in diffusion models.

New method aligns diffusion models for inference-time properties without retraining.

The paper develops a new probabilistic framework for denoising diffusion models using free entropy and stochastic analysis.

We study convexity and monotonicity properties for prices of bonds and bond options when the short rate is modeled by a diffusion process. We provide conditions under which convexity of the price in the short rate is guaranteed. Under these conditions the price is decreasing in the drift and increasing in the volatilit…

New method controls classifier guidance in diffusion models.

We present a simple dynamical model of stock index returns which is grounded on the ability of the Cyclically Adjusted Price Earning (CAPE) valuation ratio devised by Robert Shiller to predict long-horizon performances of the market. More precisely, we discuss a discrete time dynamics in which the return growth depends…

Upper bounds on constants for Brownian motion with sticky boundary.

Paper establishes fast convergence theory for diffusion models under minimal assumptions.

The paper improves the probability flow ODE sampler for faster sampling of natural images.

This work extends diffusion models to handle heavy-tailed targets, improving score estimation and sampling guarantees.

Graph diffusion processes approximate manifold heat semigroups using graph transition matrices.

New optimal rates for score estimation improve diffusion model performance.

Algorithm learns mixtures of Gaussians efficiently using diffusion models.

Study provides convergence guarantees for discrete diffusion models on finite and infinite state spaces.

We consider a general one-factor short rate model, in which the instantaneous interest rate is driven by a univariate diffusion with time independent drift and volatility. We construct recursive formula for the coefficients of the Taylor expansion of the bond price and its logarithm around $τ=0$, where $τ$ is time to m…

We investigate the $m$-relative entropy, which stems from the Bregman divergence, on weighted Riemannian and Finsler manifolds. We prove that the displacement $K$-convexity of the $m$-relative entropy is equivalent to the combination of the nonnegativity of the weighted Ricci curvature and the $K$-convexity of the weig…

The article examines entropy-information inequalities for continuous-time Markov chains under curvature-dimension conditions.

This work establishes near-minimax optimal guarantees for ODE-based samplers under mild assumptions.

New method calibrates stochastic reduced-order models from data efficiently.

Non-negative curvature affects Markov chains' mixing and expansion properties.