arXiv research

Study finds conditions for global minimizers on curved manifolds with fast diffusion and nonlocal interactions.

A new method speeds up sampling in diffusion models.

Efficiently handles contextual bandits with diffusion models.

Improved diffusion sampling for inverse problems with faster and more robust inference.

SiD distills pretrained diffusion models into a fast one-step generator.

Finite-time extinction and smoothing effects in fractional fast diffusion on manifolds.

SA-Solver improves stochastic sampling from DPMs.

Improved diffusion model generation speed with speculative sampling.

Smooth convergence shown for curve diffusion flows.

We consider gradient estimates to positive solutions of porous medium equations and fast diffusion equations: $u_t=Δ_φ(u^p)$ associated with the Witten Laplacian on Riemannian manifolds. Under the assumption that the $m$-dimensional Bakry-Emery Ricci curvature is bounded from below, we obtain gradient estimates which…

New method for fast inference in diffusion models.

The paper derives gradient estimates for porous medium and fast diffusion equations on metric measure spaces.

A fast method approximates likelihood scores for noisy linear inverse problems.

ELM combines machine learning and feature engineering for anomalous diffusion detection.

Algorithm minimizes risk for multiclass classification of stochastic diffusion paths.

In this work we derive local gradient and Laplacian estimates of the Aronson-Bénilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelman's work we discove…

A fast voice conversion method using diffusion models.

WSD uses a deterministic model to accelerate diffusion-based sampling.

PRISMA uses PDE residuals for fast, robust, and accurate inference.

Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational complexity of the diffusion maps algorithm scales with the number of observations. T…

DPM-Solver speeds up DPM sampling to 10-20 function evaluations.

In this paper mechanisms of reversion - momentum transition are considered. Two basic nonlinear mechanisms are highlighted: a slow and fast bifurcation. A slow bifurcation leads to the equilibrium evolution, preceded by stability loss delay of a control parameter. A single order parameter is introduced by Markovian cha…

We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with …

New method speeds up diffusion models inference to sub-linear time.

Reflected Diffusion Models improve on score-based models by incorporating data constraints.

Sig-DEG speeds up diffusion models by distilling them into faster approximations.

We study the fast diffusion equation (FDE) with a linear forcing term under the Ricci flow on complete manifolds with bounded curvature and nonnegative curvature operator. We prove Aronson-Bénilan and Li-Yau-Hamilton type differential Harnack estimates for positive solutions of the FDE. In addition, we use similar meth…

Efficiently solves inverse problems with diffusion and flow models in just a few steps.

Consistency models generate high-quality samples fast and without iterative sampling.

Improved graph-based multiclass classification for multilayer data.

Surface diffusion and mean curvature flows converge to stable critical sets in flat tori.

We construct exhaustion and cut-off functions with controlled gradient and Laplacian on manifolds with Ricci curvature bounded from below by a (possibly unbounded) nonpositive function of the distance from a fixed reference point, without any assumptions on the topology or the injectivity radius. Along the way we prove…

One-step diffusion samplers reduce sampling time and computational costs.

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 …

New model reduces sampling cost in diffusion models, making them faster and applicable to real-world applications.

Fast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a new algorithm to generate tight upper bounds on the Bermudan option price witho…

FasterVoiceGrad speeds up VC by 6-7x with novel distillation.

Study well-posedness of fast diffusion equation on noncompact manifolds.

Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which results in demand for derivative products which protect the holder against high prices. To this end, in this paper we present exact and fast methodologies for the simulation of the spot price dynamics modeled as the …

LADD models improve discrete diffusion for faster language generation.

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

Stabilizes complex systems using diffusion models trained on Lyapunov functions.

In this paper we discuss the basket options valuation for a jump-diffusion model. The underlying asset prices follow some correlated local volatility diffusion processes with systematic jumps. We derive a forward partial integral differential equation (PIDE) for general stochastic processes and use the asymptotic expan…

ConDiSim uses diffusion models to approximate complex system posteriors efficiently.

Faster sampling in discrete diffusion models with predetermined transition time.

A new sampling method estimates scores without training or nested MCMC.

Bayesian inference for biochemical reaction networks using jump-diffusion approximations.

Unified framework for discrete diffusion modeling with flexible noising processes.