Related papers: Probing the Geometry of Diffusion Models with the …

Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…

Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this…

This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of…

Object tracking is a fundamental task in computer vision, requiring the localization of objects of interest across video frames. Diffusion models have shown remarkable capabilities in visual generation, making them well-suited for…

Proteins play a critical role in carrying out biological functions, and their 3D structures are essential in determining their functions. Accurately predicting the conformation of protein side-chains given their backbones is important for…

Image stitching from different captures often results in non-rectangular boundaries, which is often considered unappealing. To solve non-rectangular boundaries, current solutions involve cropping, which discards image content, inpainting,…

Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational…

Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states…

Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric…

Rare transition events in meta-stable systems under noisy fluctuations are crucial for many non-equilibrium physical and chemical processes. In these processes, the primary contributions to reactive flux are predominantly near the…

Modality translation is inherently under-constrained, as multiple cross-modal mappings may yield the same marginals. Recent work has shown that diffusion bridges are effective for this task. However, most existing approaches rely on fully…

Data scarcity in medical imaging poses significant challenges due to privacy concerns. Diffusion models, a recent generative modeling technique, offer a potential solution by generating synthetic and realistic data. However, questions…

We introduce a methodology for performing parameter inference in high-dimensional, non-linear diffusion processes. We illustrate its applicability for obtaining insights into the evolution of and relationships between species, including…

Diffusion models have achieved impressive success in high-fidelity image generation but suffer from slow sampling due to their inherently iterative denoising process. While recent one-step methods accelerate inference by learning direct…

This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used with success for analyzing complex engineering systems. The…

A central problem in biology is to understand how organisms evolve and adapt to their environment by acquiring variations in the observable characteristics or traits of species across the tree of life. With the growing availability of…

We present a novel method for exemplar-based image translation, called matching interleaved diffusion models (MIDMs). Most existing methods for this task were formulated as GAN-based matching-then-generation framework. However, in this…

This work presents a comprehensive framework for enhanced diffusion modeling in fluid-structure interactions by combining the Immersed Boundary Method (IBM) with stochastic trajectories and high-order spectral boundary conditions. Using…

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview…

Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent…