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Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary…

Score-based diffusion models have recently emerged as state-of-the-art generative models for a variety of data modalities. Nonetheless, it remains unclear how to adapt these models to generate long multivariate time series. Viewing a time…

Diffusion models have seen rapid adoption in robotic imitation learning, enabling autonomous execution of complex dexterous tasks. However, action synthesis is often slow, requiring many steps of iterative denoising, limiting the extent to…

Modelling partial differential equations (PDEs) is of crucial importance in science and engineering, and it includes tasks ranging from forecasting to inverse problems, such as data assimilation. However, most previous numerical and machine…

Diffusion models have achieved remarkable success in generative modeling. However, this study confirms the existence of overfitting in diffusion model training, particularly in data-limited regimes. To address this challenge, we propose…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…

Recent score-based diffusion models (SBDMs) show promising results in unpaired image-to-image translation (I2I). However, existing methods, either energy-based or statistically-based, provide no explicit form of the interfered intermediate…

Despite its widespread use in materials science, conventional molecular dynamics (MD) simulations are severely constrained by timescale limitations. To address this shortcoming, we propose an empirical formulation of accelerated MD method,…

Diffusion models achieve high-quality image generation but are limited by slow iterative sampling. Distillation methods alleviate this by enabling one- or few-step generation. Flow matching, originally introduced as a distinct framework,…

Score-based diffusion models (SBDM) have recently emerged as state-of-the-art approaches for image generation. Existing SBDMs are typically formulated in a finite-dimensional setting, where images are considered as tensors of finite size.…

Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…

The proposed BSDE-based diffusion model represents a novel approach to diffusion modeling, which extends the application of stochastic differential equations (SDEs) in machine learning. Unlike traditional SDE-based diffusion models, our…

By leveraging the text-to-image diffusion priors, score distillation can synthesize 3D contents without paired text-3D training data. Instead of spending hours of online optimization per text prompt, recent studies have been focused on…

Flow Matching (FM) policies have emerged as an efficient backbone for robotic control, offering fast and expressive action generation that underpins recent large-scale embodied AI systems. However, FM policies trained via imitation learning…

Commonly used optimization algorithms often show a trade-off between good generalization and fast training times. For instance, stochastic gradient descent (SGD) tends to have good generalization; however, adaptive gradient methods have…

Molecular dynamics (MD) simulations remain the gold standard for studying protein dynamics, but their computational cost limits access to biologically relevant timescales. Recent generative models have shown promise in accelerating…

Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these…

Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting…