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Optimal transport (OT) has recently been shown as a promising criterion for unsupervised restoration when no explicit prior model is available. Despite its theoretical appeal, OT still significantly falls short of supervised methods on…

We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…

Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…

Face representation in the wild is extremely hard due to the large scale face variations. To this end, some deep convolutional neural networks (CNNs) have been developed to learn discriminative feature by designing properly margin-based…

Diffusion models have demonstrated exceptional capabilities in generating high-fidelity images but typically suffer from inefficient sampling. Many solver designs and noise scheduling strategies have been proposed to dramatically improve…

Recently, diffusion models have gained popularity and attention in trajectory optimization due to their capability of modeling multi-modal probability distributions. However, addressing nonlinear equality constraints, i.e, dynamic…

Out-of-distribution (OOD) detection is crucial for the reliable deployment of machine learning models in real-world scenarios, enabling the identification of unknown samples or objects. A prominent approach to enhance OOD detection…

Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of…

Recent studies have shown that the denoising process in (generative) diffusion models can induce meaningful (discriminative) representations inside the model, though the quality of these representations still lags behind those learned…

Though generative adversarial networks (GANs) areprominent models to generate realistic and crisp images,they often encounter the mode collapse problems and arehard to train, which comes from approximating the intrinsicdiscontinuous…

Diffusion models have significantly improved the quality and diversity of audio generation but are hindered by slow inference speed. Rectified flow enhances inference speed by learning straight-line ordinary differential equation (ODE)…

Trajectory generation for mobile robots in unstructured environments faces a critical dilemma: balancing kinematic smoothness for safe execution with terminal precision for fine-grained tasks. Existing generative planners often struggle…

Pre-training neural operators on diverse partial differential equation (PDE) datasets has emerged as a promising direction for building general-purpose surrogate models in scientific machine learning. However, the inherent complexity and…

Diffusion models have demonstrated exceptional capabilities in generating high-fidelity images. However, their iterative denoising process results in significant computational overhead during inference, limiting their practical deployment…

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set…

The efficient Test-Time Scaling (TTS) paradigm offers a promising perspective for enhancing the generation performance of diffusion models. However, current solutions are limited to a static, pre-defined noise pool and suffer from…

Few-Shot classification aims at solving problems that only a few samples are available in the training process. Due to the lack of samples, researchers generally employ a set of training tasks from other domains to assist the target task,…

We study unsupervised generative modeling in terms of the optimal transport (OT) problem between true (but unknown) data distribution $P_X$ and the latent variable model distribution $P_G$. We show that the OT problem can be equivalently…

Diffusion distillation is a widely used technique to reduce the sampling cost of diffusion models, yet it often requires extensive training, and the student performance tends to be degraded. Recent studies show that incorporating a GAN…

Diffusion models, such as diffusion policy, have achieved state-of-the-art results in robotic manipulation by imitating expert demonstrations. While diffusion models were originally developed for vision tasks like image and video…