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In many practical scenarios, the dynamical system is not available and standard data assimilation methods are not applicable. Our objective is to construct a data-driven model for state estimation without the underlying dynamics. Instead of…

Diffusion models for continuous data gained widespread adoption owing to their high quality generation and control mechanisms. However, controllable diffusion on discrete data faces challenges given that continuous guidance methods do not…

Diffusion models have recently emerged as the dominant approach in visual generation tasks. However, the lengthy denoising chains and the computationally intensive noise estimation networks hinder their applicability in low-latency and…

Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, a set of equations which maps data to noise in a way that can significantly affect…

We present a concise, self-contained derivation of diffusion-based generative models. Starting from basic properties of Gaussian distributions (densities, quadratic expectations, re-parameterisation, products, and KL divergences), we…

We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…

Continuous data assimilation (CDA) nudges observational data into governing equations to recover the underlying flow and improve predictions. Existing rigorous CDA analyses focus primarily on incompressible flows, yet no physical flow is…

Dataset distillation provides an effective approach to reduce memory and computational costs by optimizing a compact dataset that achieves performance comparable to the full original. However, for large-scale datasets and complex deep…

Deep generative models produce data according to a learned representation, e.g. diffusion models, through a process of approximation computing possible samples. Approximation can be understood as reconstruction and the large datasets used…

We consider a decision maker who must choose an action in order to maximize a reward function that depends also on an unknown parameter {\Theta}. The decision maker can delay taking the action in order to experiment and gather additional…

Sampling efficiently from a target unnormalized probability density remains a core challenge, with relevance across countless high-impact scientific applications. A promising approach towards this challenge is the design of amortized…

Recently, motivated by the outstanding achievements of diffusion models, the diffusion process has been employed to strengthen representation learning in recommendation systems. Most diffusion-based recommendation models typically utilize…

Recent studies on inverse problems have proposed posterior samplers that leverage the pre-trained diffusion models as powerful priors. These attempts have paved the way for using diffusion models in a wide range of inverse problems.…

Deep learning (DL) methods typically require large datasets to effectively learn data distributions. However, in the medical field, data is often limited in quantity, and acquiring labeled data can be costly. To mitigate this data scarcity,…

This paper proposes a novel particle filter for tracking time-varying states of multiple targets jointly from superpositional data, which depend on the sum of contributions of all targets. Many conventional tracking methods rely on…

Diffusion-based robot navigation policies trained on large-scale imitation learning datasets, can generate multi-modal trajectories directly from the robot's visual observations, bypassing the traditional localization-mapping-planning…

We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the…

Medical diagnosis assistant (MDA) aims to build an interactive diagnostic agent to sequentially inquire about symptoms for discriminating diseases. However, since the dialogue records used to build a patient simulator are collected…

State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state…

Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In…