Using image models naively for solving inverse video problems often suffers from flickering, texture-sticking, and temporal inconsistency in generated videos. To tackle these problems, in this paper, we view frames as continuous functions in the 2D space, and videos as a sequence of continuous warping transformations between different frames. This perspective allows us to train function space diffusion models only on **images** and utilize them to solve temporally correlated inverse problems. The function space diffusion models need to be equivariant with respect to the underlying spatial transformations. To ensure temporal consistency, we introduce a simple post-hoc test-time guidance towards (self)-equivariant solutions.

In this paper, we propose a novel framework for solving high-definition video inverse problems using latent image diffusion models. Building on recent advancements in spatio-temporal optimization for video inverse problems using image diffusion models, our approach leverages latent-space diffusion models to achieve enhanced video quality and resolution. To address the high computational demands of processing high-resolution frames, we introduce a pseudo-batch consistent sampling strategy, allowing efficient operation on a single GPU. Additionally, to improve temporal consistency, we present batch-consistent inversion, an initialization technique that incorporates informative latents from the measurement frame. By integrating with SDXL, our framework achieves state-of-the-art video reconstruction across a wide range of spatio-temporal inverse problems, including complex combinations of frame averaging and various spatial degradations, such as deblurring, super-resolution, and inpainting. Unlike previous methods, our approach supports multiple aspect ratios (landscape, vertical, and square) and delivers HD-resolution reconstructions (exceeding 1280x720) in under 2.5 minutes on a single NVIDIA 4090 GPU.

Recently, diffusion model-based inverse problem solvers (DIS) have emerged as state-of-the-art approaches for addressing inverse problems, including image super-resolution, deblurring, inpainting, etc. However, their application to video inverse problems arising from spatio-temporal degradation remains largely unexplored due to the challenges in training video diffusion models. To address this issue, here we introduce an innovative video inverse solver that leverages only image diffusion models. Specifically, by drawing inspiration from the success of the recent decomposed diffusion sampler (DDS), our method treats the time dimension of a video as the batch dimension of image diffusion models and solves spatio-temporal optimization problems within denoised spatio-temporal batches derived from each image diffusion model. Moreover, we introduce a batch-consistent diffusion sampling strategy that encourages consistency across batches by synchronizing the stochastic noise components in image diffusion models. Our approach synergistically combines batch-consistent sampling with simultaneous optimization of denoised spatio-temporal batches at each reverse diffusion step, resulting in a novel and efficient diffusion sampling strategy for video inverse problems. Experimental results demonstrate that our method effectively addresses various spatio-temporal degradations in video inverse problems, achieving state-of-the-art reconstructions. Project page: https://solving-video-inverse.github.io/main/