SSI-DM: Singularity Skipping Inversion of Diffusion Models

Inverting real images into the noise space is essential for editing tasks using diffusion models, yet existing methods produce non-Gaussian noise with poor editability due to the inaccuracy in early noising steps. We identify the root cause: a mathematical singularity that renders inversion fundamentally ill-posed. We propose Singularity Skipping Inversion of Diffusion Models (SSI-DM), which bypasses this singular region by adding small noise before standard inversion. This simple approach produces inverted noise with natural Gaussian properties while maintaining reconstruction fidelity. As a plug-and-play technique compatible with general diffusion models, our method achieves superior performance on public image datasets for reconstruction and interpolation tasks, providing a principled and efficient solution to diffusion model inversion.

Quanta Video Restoration

The proliferation of single-photon image sensors has opened the door to a plethora of high-speed and low-light imaging applications. However, data collected by these sensors are often 1-bit or few-bit, and corrupted by noise and strong motion. Conventional video restoration methods are not designed to handle this situation, while specialized quanta burst algorithms have limited performance when the number of input frames is low. In this paper, we introduce Quanta Video Restoration (QUIVER), an end-to-end trainable network built on the core ideas of classical quanta restoration methods, i.e., pre-filtering, flow estimation, fusion, and refinement. We also collect and publish I2-2000FPS, a high-speed video dataset with the highest temporal resolution of 2000 frames-per-second, for training and testing. On simulated and real data, QUIVER outperforms existing quanta restoration methods by a significant margin. Code and dataset available at https://github.com/chennuriprateek/Quanta_Video_Restoration-QUIVER-

ODE-DPS: ODE-based Diffusion Posterior Sampling for Inverse Problems in Partial Differential Equation

In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired data or necessitate retraining neural networks for modifications in the conditions of the inverse problem, significantly reducing the efficiency of inversion and limiting its applicability. To overcome this challenge, in this paper, leveraging the score-based generative diffusion model, we introduce a novel unsupervised inversion methodology tailored for solving inverse problems arising from PDEs. Our approach operates within the Bayesian inversion framework, treating the task of solving the posterior distribution as a conditional generation process achieved through solving a reverse-time stochastic differential equation. Furthermore, to enhance the accuracy of inversion results, we propose an ODE-based Diffusion Posterior Sampling inversion algorithm. The algorithm stems from the marginal probability density functions of two distinct forward generation processes that satisfy the same Fokker-Planck equation. Through a series of experiments involving various PDEs, we showcase the efficiency and robustness of our proposed method.