Related papers: On the Trajectory Regularity of ODE-based Diffusio…
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past decade as uncertainty-aware numerical integrators. They typically proceed by assuming a functional prior to the ODE solution, which is then…
While current generative models have achieved promising performances in time-series synthesis, they either make strong assumptions on the data format (e.g., regularities) or rely on pre-processing approaches (e.g., interpolations) to…
Learning dynamical systems from sparse observations is critical in numerous fields, including biology, finance, and physics. Even if tackling such problems is standard in general information fusion, it remains challenging for contemporary…
Accurate forecasting of spatiotemporal data remains challenging due to complex spatial dependencies and temporal dynamics. The inherent uncertainty and variability in such data often render deterministic models insufficient, prompting a…
Diffusion models typically generate data through a fixed denoising trajectory that is shared across all samples. However, generation targets can differ in complexity, suggesting that a single pre-defined diffusion process may not be optimal…
Diffusion models have established themselves as state-of-the-art generative models across various data modalities, including images and videos, due to their ability to accurately approximate complex data distributions. Unlike traditional…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
Continuous normalizing flows (CNFs) and diffusion models (DMs) generate high-quality data from a noise distribution. However, their sampling process demands multiple iterations to solve an ordinary differential equation (ODE) with high…
Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…
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…
Learning probabilistic models that can estimate the density of a given set of samples, and generate samples from that density, is one of the fundamental challenges in unsupervised machine learning. We introduce a new generative model based…
Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…
Score-based generative models are a popular class of generative modelling techniques relying on stochastic differential equations (SDE). From their inception, it was realized that it was also possible to perform generation using ordinary…
Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE…
Diffusion models (DMs) excel in unconditional generation, as well as on applications such as image editing and restoration. The success of DMs lies in the iterative nature of diffusion: diffusion breaks down the complex process of mapping…
Score distillation sampling (SDS) and its variants have greatly boosted the development of text-to-3D generation, but are vulnerable to geometry collapse and poor textures yet. To solve this issue, we first deeply analyze the SDS and find…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
We investigate the use of diffusion models as neural density estimators. The current approach to this problem involves converting the generative process to a smooth flow, known as the Probability Flow ODE. The log density at a given sample…