Jeongsol Kim

Imaging through scattering is challenging, as even a thin layer can randomly perturb light propagation and obscure hidden objects. Accurate closed-form modeling of forward scattering remains difficult, particularly for dynamically varying or thick layers. Here, we introduce a plug-and-play inverse solver based on video diffusion models with a physically grounded forward model tailored to dynamic scattering layers. Our method extends Diffusion Posterior Sampling (DPS) to the spatio-temporal domain, thereby capturing statistical correlations between video frames and scattered signals more effectively. Leveraging these temporal correlations, our approach recovers high-resolution spatial details that spatial-only methods typically fail to reconstruct. We also propose an inference-time optimization with a lightweight mapping network, enabling joint estimation of low-dimensional forward-model parameters without additional training. This joint optimization significantly enhances adaptability to unknown, time-varying degradations, making our method suitable for blind inverse scattering problems. We validate across diverse conditions, including different scene types, layer thicknesses, and scene-layer distances. And real-world experiments using multiple datasets confirm the robustness and effectiveness of our approach, even under real noise and forward-model approximation mismatches. Finally, we validate our method as a general video-restoration framework across dehazing, deblurring, inpainting, and blind restoration under complex optical aberrations.

Using diffusion priors to solve inverse problems in imaging have significantly matured over the years. In this chapter, we review the various different approaches that were proposed over the years. We categorize the approaches into the more classic explicit approximation approaches and others, which include variational inference, sequential monte carlo, and decoupled data consistency. We cover the extension to more challenging situations, including blind cases, high-dimensional data, and problems under data scarcity and distribution mismatch. More recent approaches that aim to leverage multimodal information through texts are covered. Through this chapter, we aim to (i) distill the common mathematical threads that connect these algorithms, (ii) systematically contrast their assumptions and performance trade-offs across representative inverse problems, and (iii) spotlight the open theoretical and practical challenges by clarifying the landscape of diffusion model based inverse problem solvers.

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 inverse problem solving has been extensively explored using diffusion models, it has not been rigorously examined within the broader context of flow models. Therefore, here we extend the diffusion inverse solvers (DIS) - which perform posterior sampling by combining a denoising diffusion prior with an likelihood gradient - into the flow framework. Specifically, by driving the flow-version of Tweedie's formula, we decompose the flow ODE into two components: one for clean image estimation and the other for noise estimation. By integrating the likelihood gradient and stochastic noise into each component, respectively, we demonstrate that posterior sampling for inverse problem solving can be effectively achieved using flows. Our proposed solver, Flow-Driven Posterior Sampling (FlowDPS), can also be seamlessly integrated into a latent flow model with a transformer architecture. Across four linear inverse problems, we confirm that FlowDPS outperforms state-of-the-art alternatives, all without requiring additional training.

Diffusion models (DMs), which enable both image generation from noise and inversion from data, have inspired powerful unpaired image-to-image (I2I) translation algorithms. However, they often require a larger number of neural function evaluations (NFEs), limiting their practical applicability. In this paper, we tackle this problem with Schrodinger Bridges (SBs), which are stochastic differential equations (SDEs) between distributions with minimal transport cost. We analyze the probability flow ordinary differential equation (ODE) formulation of SBs, and observe that we can decompose its vector field into a linear combination of source predictor, target predictor, and noise predictor. Inspired by this observation, we propose Latent Schrodinger Bridges (LSBs) that approximate the SB ODE via pre-trained Stable Diffusion, and develop appropriate prompt optimization and change of variables formula to match the training and inference between distributions. We demonstrate that our algorithm successfully conduct competitive I2I translation in unsupervised setting with only a fraction of computation cost required by previous DM-based I2I methods.

Despite the remarkable performance of text-to-image diffusion models in image generation tasks, recent studies have raised the issue that generated images sometimes cannot capture the intended semantic contents of the text prompts, which phenomenon is often called semantic misalignment. To address this, here we present a novel energy-based model (EBM) framework for adaptive context control by modeling the posterior of context vectors. Specifically, we first formulate EBMs of latent image representations and text embeddings in each cross-attention layer of the denoising autoencoder. Then, we obtain the gradient of the log posterior of context vectors, which can be updated and transferred to the subsequent cross-attention layer, thereby implicitly minimizing a nested hierarchy of energy functions. Our latent EBMs further allow zero-shot compositional generation as a linear combination of cross-attention outputs from different contexts. Using extensive experiments, we demonstrate that the proposed method is highly effective in handling various image generation tasks, including multi-concept generation, text-guided image inpainting, and real and synthetic image editing. Code: https://github.com/EnergyAttention/Energy-Based-CrossAttention.

Diffusion model-based inverse problem solvers have shown impressive performance, but are limited in speed, mostly as they require reverse diffusion sampling starting from noise. Several recent works have tried to alleviate this problem by building a diffusion process, directly bridging the clean and the corrupted for specific inverse problems. In this paper, we first unify these existing works under the name Direct Diffusion Bridges (DDB), showing that while motivated by different theories, the resulting algorithms only differ in the choice of parameters. Then, we highlight a critical limitation of the current DDB framework, namely that it does not ensure data consistency. To address this problem, we propose a modified inference procedure that imposes data consistency without the need for fine-tuning. We term the resulting method data Consistent DDB (CDDB), which outperforms its inconsistent counterpart in terms of both perception and distortion metrics, thereby effectively pushing the Pareto-frontier toward the optimum. Our proposed method achieves state-of-the-art results on both evaluation criteria, showcasing its superiority over existing methods. Code is available at https://github.com/HJ-harry/CDDB