Align & Invert: Solving Inverse Problems with Diffusion and Flow-based Models via Representational Alignment

Enforcing alignment between the internal representations of diffusion or flow-based generative models and those of pretrained self-supervised encoders has recently been shown to provide a powerful inductive bias, improving both convergence and sample quality. In this work, we extend this idea to inverse problems, where pretrained generative models are employed as priors. We propose applying representation alignment (REPA) between diffusion or flow-based models and a pretrained self-supervised visual encoder, such as DINOv2, to guide the reconstruction process at inference time. Although ground-truth signals are unavailable in inverse problems, we show that aligning model representations with approximate target features can substantially enhance reconstruction fidelity and perceptual realism. We provide theoretical results showing (a) the relation between the REPA regularization and a divergence measure in the DINOv2 embedding space, and (b) how REPA updates steer the model's internal representations toward those of the clean image. These results offer insights into the role of REPA in improving perceptual fidelity. Finally, we demonstrate the generality of our approach by integrating it into multiple state-of-the-art inverse problem solvers. Extensive experiments on super-resolution, box inpainting, Gaussian deblurring, and motion deblurring confirm that our method consistently improves reconstruction quality across tasks, while also providing substantial efficiency gains by reducing the number of required discretization steps without compromising the performance of the underlying solver.