相关论文: Probability-Flow ODE in Infinite-Dimensional Funct…
Continuous diffusion models are commonly acknowledged to display a deterministic probability flow, whereas discrete diffusion models do not. In this paper, we aim to establish the fundamental theory for the probability flow of discrete…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
In recent years, diffusion-based generative models have demonstrated remarkable performance in speech conversion, including Denoising Diffusion Probabilistic Models (DDPM) and others. However, the advantages of these models come at the cost…
Score-based diffusion models have recently been extended to infinite-dimensional function spaces, with uses such as inverse problems arising from partial differential equations. In the Bayesian formulation of inverse problems, the aim is to…
Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…
We introduce a class of jump-diffusions, called holomorphic, of which the well-known classes of affine and polynomial processes are particular instances. The defining property concerns the extended generator, which is required to map a…
The design space of discrete-space diffusion or flow generative models are significantly less well-understood than their continuous-space counterparts, with many works focusing only on a simple masked construction. In this work, we aim to…
Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspired by the optimal…
Diffusion Probabilistic Models (DPMs) have shown remarkable potential in image generation, but their sampling efficiency is hindered by the need for numerous denoising steps. Most existing solutions accelerate the sampling process by…
We consider the problem of optimization of cost functionals on the infinite-dimensional manifold of diffeomorphisms. We present a new class of optimization methods, valid for any optimization problem setup on the space of diffeomorphisms by…
We present a new class of integrators for stiff PDEs. These integrators are generalizations of FLow AVeraging integratORS (FLAVORS) for stiff ODEs and SDEs introduced in [Tao, Owhadi and Marsden 2010] with the following properties: (i)…
We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…
The diffusion models including Denoising Diffusion Probabilistic Models (DDPM) and score-based generative models have demonstrated excellent performance in speech synthesis tasks. However, its effectiveness comes at the cost of numerous…
The novel functional dimensional regularization (FDR) scheme has proven capable of yielding results that are competitive with the state-of-the-art in the computation of critical exponents in $d=3$, while also reproducing those from the…
Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…
Super-diffusion, characterized by a spreading rate $t^{1/\alpha}$ of the probability density function $p(x,t) = t^{-1/\alpha} p \left( t^{-1/\alpha} x , 1 \right)$, where $t$ is time, may be modeled by space-fractional diffusion equations…
Longstanding problems regarding the causality of the diffusion equation are resolved through a class of exact solutions. A universal differential solution for diffusive processes is derived that is causal and exact at any analytic point in…
Out-of-distribution (OOD) detection is critical for ensuring the reliability of deep learning systems, particularly in safety-critical applications. Likelihood-based deep generative models have historically faced criticism for their…
We present theoretical convergence guarantees for ODE-based generative models, specifically flow matching. We use a pre-trained autoencoder network to map high-dimensional original inputs to a low-dimensional latent space, where a…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…