Related papers: A Free Probabilistic Framework for Denoising Diffu…
Scenario-based probabilistic forecasts have become vital for decision-makers in handling intermittent renewable energies. This paper presents a recent promising deep learning generative approach called denoising diffusion probabilistic…
Despite the remarkable empirical success of score-based diffusion models, their statistical guarantees remain underdeveloped. Existing analyses often provide pessimistic convergence rates that do not reflect the intrinsic low-dimensional…
This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…
Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is…
Denoising diffusion models have spurred significant gains in density modeling and image generation, precipitating an industrial revolution in text-guided AI art generation. We introduce a new mathematical foundation for diffusion models…
This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…
We analyze the time reversed dynamics of generative diffusion models. If the exact empirical score function is used in a regime of large dimension and exponentially large number of samples, these models are known to undergo transitions…
Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and restores it through a trainable model. This framework enables…
Local climate information is crucial for impact assessment and decision-making, yet coarse global climate simulations cannot capture small-scale phenomena. Current statistical downscaling methods infer these phenomena as temporally…
Score-based generative modeling, implemented through probability flow ODEs, has shown impressive results in numerous practical settings. However, most convergence guarantees rely on restrictive regularity assumptions on the target…
Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting…
High-dimensional dynamical systems projected onto a reduced-order model cease to be deterministic and are best described by probability distributions in state space. Their equations of motion map onto an evolution operator with a…
What is the optimal way to approximate a high-dimensional diffusion process by one in which the coordinates are independent? This paper presents a construction, called the \emph{independent projection}, which is optimal for two natural…
We propose self-diffusion, a novel framework for solving inverse problems without relying on pretrained generative models. Traditional diffusion-based approaches require training a model on a clean dataset to learn to reverse the forward…
Diffusion models represent a class of generative models that produce data by denoising a sample corrupted by white noise. Despite the success of diffusion models in computer vision, audio synthesis, and point cloud generation, so far they…
This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…
A novel probabilistic framework for modelling anomalous diffusion is presented. The resulting process is Markovian, non-homogeneous, non-stationary, non-ergodic, and state-dependent. The fundamental law governing this process is driven by…
Diffusion models are one of the most important families of deep generative models. In this note, we derive a quantitative upper bound on the Wasserstein distance between the data-generating distribution and the distribution learned by a…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…
Denoising diffusion probabilistic models (DDPMs) have emerged as powerful generative models for complex distributions, yet their use in arbitrage-free derivative pricing remains largely unexplored. Financial asset prices are naturally…