Score Distillation Beyond Acceleration: Generative Modeling from Corrupted Data

Learning generative models directly from corrupted observations is a long standing challenge across natural and scientific domains. We introduce Restoration Score Distillation (RSD), a unified framework for learning high fidelity, one step generative models using only degraded data and the mapping $A$ may be the identity or a non invertible corruption operator (e.g., blur, masking, subsampling, Fourier acquisition). RSD first pretrains a corruption aware diffusion teacher on the observed measurements, then distills it into an efficient one step generator whose samples are statistically closer to the clean distribution p_X. The framework subsumes identity corruption (denoising task) as a special case of our general formulation. Empirically, RSD consistently reduces Frechet Inception Distance (FID) relative to corruption aware diffusion teachers across noisy generation (CIFAR 10, FFHQ, CelebA HQ, AFHQ v2), image restoration (Gaussian deblurring, random inpainting, super resolution, and mixtures with additive noise), and multi coil MRI without access to any clean images. The distilled generator inherits one step sampling efficiency, yielding up to 30x speedups over multi step diffusion while surpassing the teachers after substantially fewer training iterations. These results establish score distillation as a practical tool for generative modeling from corrupted data, not merely for acceleration. We provide theoretical support for the use of distillation in enhancing generation quality in the Appendix.