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Protein structure prediction is pivotal for understanding the structure-function relationship of proteins, advancing biological research, and facilitating pharmaceutical development and experimental design. While deep learning methods and…

Anomalous diffusion occurs in a wide range of systems, including protein transport within cells, animal movement in complex habitats, pollutant dispersion in groundwater, and nanoparticle motion in synthetic materials. Accurately estimating…

We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…

Improving the understanding of diffusive processes in networks with complex topologies is one of the main challenges of today's complexity science. Each network possesses an intrinsic diffusive potential that depends on its structural…

In recent years neural networks have achieved impressive results on many technological and scientific tasks. Yet, the mechanism through which these models automatically select features, or patterns in data, for prediction remains unclear.…

The diffusion properties of self-propelled particles which move at constant speed and, in addition, reverse their direction of motion repeatedly are investigated. The internal dynamics of particles triggering these reversal processes is…

This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. While diffusion models are renowned for their generative modeling capabilities,…

In this work, we investigate an intriguing and prevalent phenomenon of diffusion models which we term as "consistent model reproducibility": given the same starting noise input and a deterministic sampler, different diffusion models often…

Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…

Diffusion Policy (DP) enables robots to learn complex behaviors by imitating expert demonstrations through action diffusion. However, in practical applications, hardware limitations often degrade data quality, while real-time constraints…

Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…

Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the…

Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of…

In this paper, we investigate a deep learning method for predicting path-dependent processes based on discretely observed historical information. This method is implemented by considering the prediction as a nonparametric regression and…

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data.…

Diffusion models generate high-dimensional data such as images by learning a process that gradually removes noise from corrupted data. Recent studies have shown that the backward dynamics of diffusion models exhibit two characteristic…

Recent years have witnessed the rapid development of acceleration techniques for diffusion models, especially caching-based acceleration methods. These studies seek to answer two fundamental questions: "When to cache" and "How to use…

Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…

Accurate modeling of robot dynamics is essential for model-based control, yet remains challenging under distributional shifts and real-time constraints. In this work, we formulate system identification as an in-context meta-learning problem…