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Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of…

Generative modelling is a key tool in unsupervised machine learning which has achieved stellar success in recent years. Despite this huge success, even the best generative models such as Generative Adversarial Networks (GANs) and…

We present a trajectory generation framework for control of wheeled vehicles under steering actuator constraints. The motivation is smooth autonomous driving of heavy vehicles. The key idea is to take into account rate, and additionally,…

We tackle the problem of sampling from intractable high-dimensional density functions, a fundamental task that often appears in machine learning and statistics. We extend recent sampling-based approaches that leverage controlled stochastic…

Continuous-time generative models, such as Flow Matching (FM), construct probability paths to transport between one distribution and another through the simulation-free learning of the neural ordinary differential equations (ODEs). During…

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…

Reliable and efficient trajectory generation methods are a fundamental need for autonomous dynamical systems of tomorrow. The goal of this article is to provide a comprehensive tutorial of three major convex optimization-based trajectory…

We introduce a new paradigm for generative modeling built on Continuous Normalizing Flows (CNFs), allowing us to train CNFs at unprecedented scale. Specifically, we present the notion of Flow Matching (FM), a simulation-free approach for…

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This…

Diffusion probabilistic models (DPMs) have shown remarkable performance in high-resolution image synthesis, but their sampling efficiency is still to be desired due to the typically large number of sampling steps. Recent advancements in…

Simulations of turbulent flows in 3D are one of the most expensive simulations in computational fluid dynamics (CFD). Many works have been written on surrogate models to replace numerical solvers for fluid flows with faster, learned,…

Diffusion models have demonstrated great potential in generating high-quality content for images, natural language, protein domains, etc. However, how to perform user-preferred targeted generation via diffusion models with only black-box…

Autoregressive models have achieved remarkable success across various domains, yet their performance in 3D shape generation lags significantly behind that of diffusion models. In this paper, we introduce OctGPT, a novel multiscale…

Deep neural networks achieve superior performance for learning from independent and identically distributed (i.i.d.) data. However, their performance deteriorates significantly when handling out-of-distribution (OoD) data, where the…

Diffusion and flow-matching models achieve remarkable generative performance but at the cost of many sampling steps, this slows inference and limits applicability to time-critical tasks. The ReFlow procedure can accelerate sampling by…

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…

Current performance-driven building design methods are not widely adopted outside the research field for several reasons that make them difficult to integrate into a typical design process. In the early design phase, in particular, the…

Diffusion models (DMs) are a powerful generative framework that have attracted significant attention in recent years. However, the high computational cost of training DMs limits their practical applications. In this paper, we start with a…

Diffusion Models (DMs) have achieved remarkable progress in generative modeling. However, the mismatch between the forward terminal distribution and reverse initial distribution introduces prior error, leading to deviations of sampling…

This paper develops a generative model by minimizing the second-order Wasserstein loss (the $W_2$ loss) through a distribution-dependent ordinary differential equation (ODE), whose dynamics involves the Kantorovich potential associated with…