Related papers: Conditioning Diffusions Using Malliavin Calculus
This study presents a generative optimization framework that builds on a fine-tuned diffusion model and reward-directed sampling to generate high-performance engineering designs. The framework adopts a parametric representation of the…
Analogue to the well-known Langevin Monte Carlo method, in this article we provide a method to sample from a target distribution \(\pi\) by simulating a solution of a stochastic differential equation. Hereby, the stochastic differential…
This work concerns continuous-time, continuous-space stochastic dynamical systems described by stochastic differential equations (SDE). It presents a new approach to compute probabilistic safety regions, namely sets of initial conditions of…
Recent advances in diffusion models have demonstrated their strong capabilities in generating high-fidelity samples from complex distributions through an iterative refinement process. Despite the empirical success of diffusion models in…
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning. In these applications, conditional diffusion models incorporate…
Using Malliavin calculus techniques, we derive an analytical formula for the price of European options, for any model including local volatility and Poisson jump process. We show that the accuracy of the formula depends on the smoothness of…
An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different…
We study the optimal dividend problem for a firm's manager who has partial information on the profitability of the firm. The problem is formulated as one of singular stochastic control with partial information on the drift of the underlying…
Literature is full of inference techniques developed to estimate the parameters of stochastic dynamical systems driven by the well-known Brownian noise. Such diffusion models are often inappropriate models to properly describe the dynamics…
We study the problem of training diffusion and flow generative models to sample from target distributions defined by an exponential tilting of a base density; a formulation that subsumes both sampling from unnormalized densities and reward…
A novel discretization is presented for forward-backward stochastic differential equations (FBSDE) with differentiable coefficients, simultaneously solving the BSDE and its Malliavin sensitivity problem. The control process is estimated by…
Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or…
We propose a hybrid generative model for efficient sampling of high-dimensional, multimodal probability distributions for Bayesian inference. Traditional Monte Carlo methods, such as the Metropolis-Hastings and Langevin Monte Carlo sampling…
Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing…
In this paper, we focus on non-asymptotic bounds related to the Euler scheme of an ergodic diffusion with a possibly multiplicative diffusion term (non-constant diffusion coefficient). More precisely, the objective of this paper is to…
Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…
Langevin diffusion is a powerful method for nonconvex optimization, which enables the escape from local minima by injecting noise into the gradient. In particular, the temperature parameter controlling the noise level gives rise to a…
We provide theoretical convergence guarantees for score-based generative models (SGMs) such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of large-scale real-world generative models such as DALL$\cdot$E…
In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…
We study conditional generation in diffusion models under hard constraints, where generated samples must satisfy prescribed events with probability one. Such constraints arise naturally in safety-critical applications and in rare-event…