Related papers: Diffusion on the Probability Simplex

Generative diffusion processes are an emerging and effective tool for image and speech generation. In the existing methods, the underline noise distribution of the diffusion process is Gaussian noise. However, fitting distributions with…

Can continuous diffusion models bring the same performance breakthrough on natural language they did for image generation? To circumvent the discrete nature of text data, we can simply project tokens in a continuous space of embeddings, as…

We consider a generalised diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyse the probability distribution functions and we derive the mean squared displacement in $x$ and $y$ directions.…

Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain…

Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set of observations of this vector. The probability distribution…

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…

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…

Positional reasoning is the process of ordering unsorted parts contained in a set into a consistent structure. We present Positional Diffusion, a plug-and-play graph formulation with Diffusion Probabilistic Models to address positional…

A constructive approach to theory of diffusion processes is proposed, which is based on application of both the symmetry analysis and method of modelling functions. An algorithm for construction of the modelling functions is suggested. This…

The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…

The robustness of image segmentation has been an important research topic in the past few years as segmentation models have reached production-level accuracy. However, like classification models, segmentation models can be vulnerable to…

The Gumbel-Softmax is a continuous distribution over the simplex that is often used as a relaxation of discrete distributions. Because it can be readily interpreted and easily reparameterized, it enjoys widespread use. We propose a modular…

Despite the remarkable progress in generative modelling, current diffusion models lack a quantitative approach to assess image quality. To address this limitation, we propose to estimate the pixel-wise aleatoric uncertainty during the…

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…

In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…

While diffusion models have shown great success in image generation, their noise-inverting generative process does not explicitly consider the structure of images, such as their inherent multi-scale nature. Inspired by diffusion models and…

We develop diffusion-based samplers for target distributions known up to a normalising constant. To this end, we rely on the well-known diffusion path that smoothly interpolates between a simple base distribution and the target, popularised…

We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…

How do diffusion generative models convert pure noise into meaningful images? In a variety of pretrained diffusion models (including conditional latent space models like Stable Diffusion), we observe that the reverse diffusion process that…