相关论文: Construction of Diffusion Algebras

Diffusion-based generative models in SE(3)-invariant space have demonstrated promising performance in molecular conformation generation, but typically require solving stochastic differential equations (SDEs) with thousands of update steps.…

A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge of stochastic simulations is assumed. The methods are explained using illustrative examples. The article starts with the…

We introduce a new class of nonparametric prior distributions on the space of continuously varying densities, induced by Dirichlet process mixtures which diffuse in time. These select time-indexed random functions without jumps, whose…

Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that…

Machine learning models that operate on graph-structured data, such as molecular graphs or social networks, often make accurate predictions but offer little insight into why certain predictions are made. Counterfactual explanations address…

Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…

We present an accessible first course on diffusion models and flow matching for machine learning, aimed at a technical audience with no diffusion experience. We try to simplify the mathematical details as much as possible (sometimes…

This survey paper is a structured concise summary of four of our recent papers on the stochastic regularity of diffusions that are associated to regular strongly local (but not necessarily symmetric) Dirichlet forms. Here by stochastic…

A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…

We introduce a new diffusion-based approach for shape completion on 3D range scans. Compared with prior deterministic and probabilistic methods, we strike a balance between realism, multi-modality, and high fidelity. We propose DiffComplete…

Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…

Diffusion models are state-of-the-art tools for various generative tasks. Yet training these models involves estimating high-dimensional score functions, which in principle suffers from the curse of dimensionality. It is therefore important…

Diffusion models, though originally designed for generative tasks, have demonstrated impressive self-supervised representation learning capabilities. A particularly intriguing phenomenon in these models is the emergence of unimodal…

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…

Machine learning methods have been shown to be effective for weather forecasting, based on the speed and accuracy compared to traditional numerical models. While early efforts primarily concentrated on deterministic predictions, the field…

In this report, we introduce observation algebras, constructed by considering the downclosed subsets of a coherence space ordered by reverse inclusion. These may be interpreted as specifications of sets of events via some predicates with…

We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces,…

In this paper, by using the concept of positive elements of $C^*$-algebras instead of the real numbers $\mathbb{R}$, a generalization of distribution functions, with a particular focus on distance distribution functions has been introduced…

Classical $W$-algebras in higher dimensions are constructed. This is achieved by generalizing the classical Gel'fand-Dickey brackets to the commutative limit of the ring of classical pseudodifferential operators in arbitrary dimension.…