Related papers: Exact simulation of the Wright-Fisher diffusion
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
Diffusion policies are powerful visuomotor models for robotic manipulation, yet they often fail to generalize to manipulators or end-effectors unseen during training and struggle to accommodate new task requirements at inference time.…
A family of diffusion-annihilation processes is introduced, which is exactly solvable. This family contains parameters that control the diffusion- and annihilation- rates. The solution is based on the Bethe ansatz and using special boundary…
Generative modeling over discrete data has recently seen numerous success stories, with applications spanning language modeling, biological sequence design, and graph-structured molecular data. The predominant generative modeling paradigm…
We introduce a diffusion-transformer (DiT) framework for single-image reflection removal that leverages the generalization strengths of foundation diffusion models in the restoration setting. Rather than relying on task-specific…
Autoregressive video diffusion models hold promise for world simulation but are vulnerable to exposure bias arising from the train-test mismatch. While recent works address this via post-training, they typically rely on a bidirectional…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
Diffusion models have recently shown promise as powerful generative priors for inverse problems. However, conventional applications require solving the full reverse diffusion process and operating on noisy intermediate states, which poses…
Simulation of conditioned diffusion processes is an essential tool in inference for stochastic processes, data imputation, generative modelling, and geometric statistics. Whilst simulating diffusion bridge processes is already difficult on…
In the present review we survey the properties of a transcendental function of the Wright type, nowadays known as M-Wright function, entering as a probability density in a relevant class of self-similar stochastic processes that we…
Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…
The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics,…
Spatio-temporal dynamics of the evolution of population involving growth and diffusion processes can be modeled by class of partial diffusion equations (PDEs) known as reaction-diffusion systems. In this work, we developed a nonlinear…
The Bernstein operator is known as a typical example of positive linear operators which uniformly approximates continuous functions on $[0, 1]$. In the present paper, we introduce a multidimensional extension of the Bernstein operator which…
Extinction times in resampling processes are fundamental yet often intractable, as previous formulas scale as $2^M$ with the number of states $M$ present in the initial probability distribution. We solve this by treating multinomial updates…
We introduce exact methods for the simulation of sample paths of one-dimensional diffusions with a discontinuity in the drift function. Our procedures require the simulation of finite-dimensional candidate draws from probability laws…
Full waveform inversion (FWI) has the potential to provide high-resolution subsurface model estimations. However, due to limitations in observation, e.g., regional noise, limited shots or receivers, and band-limited data, it is hard to…
Recent Diffusion models (DMs) advancements have explored incorporating the second-order diffusion Fisher information (DF), defined as the negative Hessian of log density, into various downstream tasks and theoretical analysis. However,…
In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore…
We use the Gaussian Phase-Space Representation to solve the real-time dynamic of interacting fermions in 1D, 2D, and 3D systems. The method is exact up to a spiking point, which represents a limit on the practical simulation time. The…