Recently, various methods have been proposed to solve Image Restoration (IR) tasks using a pre-trained diffusion model leading to state-of-the-art performance. However, most of these methods assume that the degradation operator in the IR task is completely known. Furthermore, a common characteristic among these approaches is that they alter the diffusion sampling process in order to satisfy the consistency with the degraded input image. This choice has recently been shown to be sub-optimal and to cause the restored image to deviate from the data manifold. To address these issues, we propose Blind Image Restoration via fast Diffusion inversion (BIRD) a blind IR method that jointly optimizes for the degradation model parameters and the restored image. To ensure that the restored images lie onto the data manifold, we propose a novel sampling technique on a pre-trained diffusion model. A key idea in our method is not to modify the reverse sampling, \ie, not to alter all the intermediate latents, once an initial noise is sampled. This is ultimately equivalent to casting the IR task as an optimization problem in the space of the input noise. Moreover, to mitigate the computational cost associated with inverting a fully unrolled diffusion model, we leverage the inherent capability of these models to skip ahead in the forward diffusion process using large time steps. We experimentally validate BIRD on several image restoration tasks and show that it achieves state of the art performance on all of them.