Related papers: Diffusion Models as Stochastic Quantization in Lat…

Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…

This paper introduces a discrete diffusion model (DDM) framework for text-aligned speech tokenization and reconstruction. By replacing the auto-regressive speech decoder with a discrete diffusion counterpart, our model achieves…

Lattice-based stochastic simulators are commonly used to study biological reaction-diffusion processes. Some of these schemes that are based on the reaction-diffusion master equation (RDME), can simulate for extended spatial and temporal…

Diffusion models (DMs) have achieved state-of-the-art results for image synthesis tasks as well as density estimation. Applied in the latent space of a powerful pretrained autoencoder (LDM), their immense computational requirements can be…

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…

Diffusion models have been widely adopted in image generation, producing higher-quality and more diverse samples than generative adversarial networks (GANs). We introduce a latent diffusion model (LDM) for precipitation nowcasting -…

We present here the first lattice simulation of symplectic quantization, a new functional approach to quantum field theory which allows to define an algorithm to numerically sample the quantum fluctuations of fields directly in Minkowski…

Can standard continuous-time generative models represent distributions whose support is an extremely sparse, globally constrained discrete set? We study this question using completed Sudoku grids as a controlled testbed, treating them as a…

Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples…

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…

Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…

Generative diffusion models apply the concept of Langevin dynamics in physics to machine leaning, attracting a lot of interests from engineering, statistics and physics, but a complete picture about inherent mechanisms is still lacking. In…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…

Diffusion approximations are widely used in the analysis of service systems, providing tractable insights into complex models. While heavy-traffic limit theorems justify these approximations asymptotically, they do not quantify the error…

Classical diffusion models have shown superior generative results. Exploring them in the quantum domain can advance the field of quantum generative learning. This work introduces Quantum Generative Diffusion Model (QGDM) as their simple and…

Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…

Spatially-distributed, nonequilibrium chemical systems described by a Markov chain model are considered. The evolution of such systems arises from a combination of local birth-death reactive events and random walks executed by the particles…

Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…