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In many engineering and applied science domains, high-dimensional nonlinear filtering is still a challenging problem. Recent advances in score-based diffusion models offer a promising alternative for posterior sampling but require repeated…

Diffusion models have recently demonstrated an impressive ability to address inverse problems in an unsupervised manner. While existing methods primarily focus on modifying the posterior sampling process, the potential of the forward…

In this paper, we address a new problem of reversing the effect of an image filter, which can be linear or nonlinear. The assumption is that the algorithm of the filter is unknown and the filter is available as a black box. We formulate…

Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…

In light of the widespread success of generative models, a significant amount of research has gone into speeding up their sampling time. However, generative models are often sampled multiple times to obtain a diverse set incurring a cost…

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in…

Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…

Particle filters are a frequent choice for inference tasks in nonlinear and non-Gaussian state-space models. They can either be used for state inference by approximating the filtering distribution or for parameter inference by approximating…

Diffusion models are the current state of the art for generating photorealistic images. Controlling the sampling process for constrained image generation tasks such as inpainting, however, remains challenging since exact conditioning on…

Optimization methods are essential in solving complex problems across various domains. In this research paper, we introduce a novel optimization method called Gaussian Crunching Search (GCS). Inspired by the behaviour of particles in a…

We propose a robust alignment technique for Standard Fundus Images (SFIs) and Ultra-Widefield Fundus Images (UWFIs), which are challenging to align due to differences in scale, appearance, and the scarcity of distinctive features. Our…

Unified image restoration is a significantly challenging task in low-level vision. Existing methods either make tailored designs for specific tasks, limiting their generalizability across various types of degradation, or rely on training…

We propose a data-efficient, physics-aware generative framework in function space for inverse PDE problems. Existing plug-and-play diffusion posterior samplers represent physics implicitly through joint coefficient-solution modeling,…

Constructing fast samplers for unconditional diffusion and flow-matching models has received much attention recently; however, existing methods for solving inverse problems, such as super-resolution, inpainting, or deblurring, still require…

Conditional particle filters (CPFs) are powerful smoothing algorithms for general nonlinear/non-Gaussian hidden Markov models. However, CPFs can be inefficient or difficult to apply with diffuse initial distributions, which are common in…

Projection Pursuit is a classic exploratory technique for finding interesting projections of a dataset. We propose a method for recovering projections containing either Imbalanced Clusters or a Bernoulli-Rademacher distribution using a…

Recovering a signal from its degraded measurements is a long standing challenge in science and engineering. Recently, zero-shot diffusion based methods have been proposed for such inverse problems, offering a posterior sampling based…

Diffusion models have been demonstrated as strong priors for solving general inverse problems. Most existing Diffusion model-based Inverse Problem Solvers (DIS) employ a plug-and-play approach to guide the sampling trajectory with either…

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…