Pixel-Space Diffusion via Observation Operators

Pixel-space diffusion avoids the compression artifacts of latent models such as Stable Diffusion, but it is harder to optimize because conventional flow matching supervises the entire clean image at every noise level. This paper identifies that conflict as a scale–time mismatch: coarse structure is predictable under heavy noise, while fine detail emerges later. Observation Operator Diffusion replaces the fixed target with a time-indexed trajectory of Gaussian–Lanczos observations, smoothly progressing from low-pass structure to the full image, and adds the derivative of that trajectory to the velocity target. Its GL-CoDA decoder extends the same coarse-to-fine principle through network depth by injecting scale-specific structural responses into a Patch-DiT backbone, while retaining REPA representation alignment and direct v prediction. On class-conditional ImageNet-1K, the 798M-parameter model reaches gFID 1.95 after 80 epochs and 1.52 after 260 epochs at 256×256 resolution, using 60 fewer epochs than the prior best pixel-space result. At 512×512, it achieves gFID 1.58, a 12.7% improvement over the previous pixel-space benchmark, with recall rising to 0.69. Ablations show the combined Gaussian–Lanczos kernel outperforming identity, Gaussian-only, and Lanczos-only supervision, supporting the claim that scale-aligned targets improve gradient signal and convergence. The work is particularly relevant to industrial image-generation efforts, including those associated with JD.com, but it does not depend on proprietary systems such as OpenAI’s Sora or Meta’s Llama.