Related papers: Modeling genome evolution with a diffusion approxi…
Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such…
Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results…
Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
This work introduces the generative fractional diffusion model for protein generation (ProT-GFDM), a novel generative framework that employs fractional stochastic dynamics for protein backbone structure modeling. This approach builds on the…
Predicting molecular conformations from molecular graphs is a fundamental problem in cheminformatics and drug discovery. Recently, significant progress has been achieved with machine learning approaches, especially with deep generative…
The Drift-Diffusion Model (DDM) is widely used in neuropsychological studies to understand the decision process by incorporating both reaction times and subjects' responses. Various models have been developed to estimate DDM parameters,…
Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…
Our goal is to extend the denoising diffusion implicit model (DDIM) to general diffusion models~(DMs) besides isotropic diffusions. Instead of constructing a non-Markov noising process as in the original DDIM, we examine the mechanism of…
The reaction-diffusion processes in a growing domain involves a dilution term that modifies the properties of the homogeneous state that, in contrast to a fixed domain, depends on time. We study how the dilution term changes the steady…
Understanding how biomarker distributions evolve over time is a central challenge in digital health and chronic disease monitoring. In diabetes, changes in the distribution of glucose measurements can reveal patterns of disease progression…
This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where…
In this article, we construct a generalization of the Blum-Fran\c{c}ois Beta-splitting model for evolutionary trees, which was itself inspired by Aldous' Beta-splitting model on cladograms. The novelty of our approach allows for asymmetric…
Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static…
Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…
Combining discrete and continuous data is an important capability for generative models. We present Discrete Flow Models (DFMs), a new flow-based model of discrete data that provides the missing link in enabling flow-based generative models…
In many situations, the gene expression signature is a unique marker of the biological state. We study the modification of the gene expression distribution function when the biological state of a system experiences a change. This change may…