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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,…

Diffusion models (DMs) have proven to be effective in modeling high-dimensional distributions, leading to their widespread adoption for representing complex priors in Bayesian inverse problems (BIPs). However, current DM-based posterior…

Diffusion MRI (dMRI) is a valuable tool to map brain microstructure and connectivity by analyzing water molecule diffusion in tissue. However, acquiring dMRI data requires to capture multiple 3D brain volumes in a short time, often leading…

3D Gaussian Splatting (3DGS) is a leading 3D scene reconstruction method, obtaining high-quality reconstruction with real-time rendering runtime performance. The main idea behind 3DGS is to represent the scene as a collection of 3D…

Diffusion models have emerged as the new state-of-the-art generative model with high quality samples, with intriguing properties such as mode coverage and high flexibility. They have also been shown to be effective inverse problem solvers,…

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…

With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…

Transparent and reflective objects, which are common in our everyday lives, present a significant challenge to 3D imaging techniques due to their unique visual and optical properties. Faced with these types of objects, RGB-D cameras fail to…

Diffusion models have achieved remarkable success in imaging inverse problems owing to their powerful generative capabilities. However, existing approaches typically rely on models trained for specific degradation types, limiting their…

We propose Amortized Posterior Sampling (APS), a novel variational inference approach for efficient posterior sampling in inverse problems. Our method trains a conditional flow model to minimize the divergence between the variational…

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…

From a Bayesian perspective, score-based diffusion solves inverse problems through joint inference, embedding the likelihood with the prior to guide the sampling process. However, this formulation fails to explain its practical behavior:…

Diffusion models have demonstrated exceptional capabilities in image restoration, yet their application to video super-resolution (VSR) faces significant challenges in balancing fidelity with temporal consistency. Our evaluation reveals a…

Diffusion models have emerged as a key pillar of foundation models in visual domains. One of their critical applications is to universally solve different downstream inverse tasks via a single diffusion prior without re-training for each…

Diffusion models have gained prominence as powerful generative tools for solving inverse problems due to their ability to model complex data distributions. However, existing methods typically rely on complete knowledge of the forward…

Diffusion models have achieved impressive results in generative tasks such as text-to-image synthesis, yet they often struggle to fully align outputs with nuanced user intent and maintain consistent aesthetic quality. Existing…

Rapid urbanization demands accurate and efficient monitoring of turbulent wind patterns to support air quality, climate resilience and infrastructure design. Traditional sparse reconstruction and sensor placement strategies face major…

Discrete diffusion models excel at visual synthesis but rely on slow, iterative decoding. Existing single-step distillation methods attempt to bypass this bottleneck, either by training auxiliary score networks that effectively double…

Planning with pretrained diffusion models has emerged as a promising approach for solving test-time guided control problems. Standard gradient guidance typically performs optimally under convex, differentiable reward landscapes. However, it…

Hallucinations are spurious structures not present in the ground truth, posing a critical challenge in medical image reconstruction, especially for data-driven conditional models. We hypothesize that combining an unconditional diffusion…