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The Diffusion Map is a nonlinear dimensionality reduction technique used to analyze high-dimensional data, with recent applications extending to datasets from the social sciences. Previous research has given little attention to how the…

Generative models such as diffusion models, excel at capturing high-dimensional distributions with diverse input modalities, e.g. robot trajectories, but are less effective at multi-step constraint reasoning. Task and Motion Planning (TAMP)…

Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…

A partial differential equation governing the global evolution of the joint probability distribution of an arbitrary number of local flow observations, drawn randomly from a control volume, is derived and applied to examples involving…

Despite the proliferation of generative models, achieving fast sampling during inference without compromising sample diversity and quality remains challenging. Existing models such as Denoising Diffusion Probabilistic Models (DDPM) deliver…

The success of Deep Learning applications critically depends on the quality and scale of the underlying training data. Generative adversarial networks (GANs) can generate arbitrary large datasets, but diversity and fidelity are limited,…

In many scientific fields imaging is used to relate a certain physical quantity to other dependent variables. Therefore, images can be considered as a map from a real-world coordinate system to the non-negative measurements being acquired.…

We argue that diffusion models' success in modeling complex distributions is, for the most part, coming from their input conditioning. This paper investigates the representation used to condition diffusion models from the perspective that…

Diffusion models exhibit excellent sample quality, but existing guidance methods often require additional model training or are limited to specific tasks. We revisit guidance in diffusion models from the perspective of variational inference…

Experiments featuring fast heat propagation, or so called "non-local" transport, were a puzzle for almost two decades. However recently it was shown, and it is recalled here, that a collective ideal MHD response of the plasma provides a…

Physics phenomena are often described by ordinary and/or partial differential equations (ODEs/PDEs), and solved analytically or numerically. Unfortunately, many real-world systems are described only approximately with missing or unknown…

Masked Diffusion Models (MDMs) have emerged as one of the most promising paradigms for generative modeling over discrete domains. It is known that MDMs effectively train to decode tokens in a random order, and that this ordering has…

Latent dynamical models are commonly used to learn the distribution of a latent dynamical process that represents a sequence of noisy data samples. However, producing samples from such models with high fidelity is challenging due to the…

With the rapid deployments of 5G and 6G networks, accurate modeling of urban radio propagation has become critical for system design and network planning. However, conventional statistical or empirical models fail to fully capture the…

Recent advances in image generation have made diffusion models powerful tools for creating high-quality images. However, their iterative denoising process makes understanding and interpreting their semantic latent spaces more challenging…

Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…

Achieving safe and stylized trajectory planning in complex real-world scenarios remains a critical challenge for autonomous driving systems. This paper proposes the SDD Planner, a diffusion-based framework designed to effectively reconcile…

Latent diffusion models offer an attractive alternative to discrete diffusion for non-autoregressive text generation by operating on continuous text representations and denoising entire sequences in parallel. The major challenge in latent…

This work addresses the task of modeling spatiotemporal traffic patterns directly from overhead imagery, which we refer to as image-driven traffic modeling. We extend this line of work and introduce a multi-modal, multi-task…

Diffusion probabilistic models (DPMs) have become the state-of-the-art in high-quality image generation. However, DPMs have an arbitrary noisy latent space with no interpretable or controllable semantics. Although there has been significant…