# Pixel-Space Diffusion via Observation Operators

arXiv: https://arxiv.org/abs/2608.21885 · HTML: https://mlsanity.com/paper/2608.21885/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 16 of its 31 references that are in the map.
- First posted on arXiv 22 Aug 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 16 of 16)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [PixelFlow: Pixel-Space Generative Models with Flow](https://mlsanity.com/paper/2504.07963/) (2025)
- [Latent Diffusion Model without Variational Autoencoder](https://mlsanity.com/paper/2510.15301/) (2025)
- [PixelDiT: Pixel Diffusion Transformers for Image Generation](https://mlsanity.com/paper/2511.20645/) (2025)
- [DeCo: Frequency-Decoupled Pixel Diffusion for End-to-End Image Generation](https://mlsanity.com/paper/2511.19365/) (2025)
- [DiP: Taming Diffusion Models in Pixel Space](https://mlsanity.com/paper/2511.18822/) (2025)
- [There is No VAE: End-to-End Pixel-Space Generative Modeling via Self-Supervised Pre-training](https://mlsanity.com/paper/2510.12586/) (2025)
- [FARMER: Flow AutoRegressive Transformer over Pixels](https://mlsanity.com/paper/2510.23588/) (2025)
- [PixelGen: Improving Pixel Diffusion with Perceptual Supervision](https://mlsanity.com/paper/2602.02493/) (2026)
- [HyperDiT: Hyper-Connected Transformers for High-Fidelity Pixel-Space Diffusion](https://mlsanity.com/paper/2605.15741/) (2026)
- [PixelU: A U-Shaped Transformer for Efficient End-to-End Pixel Diffusion](https://mlsanity.com/paper/2606.27760/) (2026)
- [Revisiting Diffusion Model Predictions Through Dimensionality](https://mlsanity.com/paper/2601.21419/) (2026)
- [FrequencyBooster: Full-Frequency Modeling for High-Fidelity Pixel Diffusion](https://mlsanity.com/paper/2605.17759/) (2026)
- [FREPix: Frequency-Heterogeneous Flow Matching for Pixel-Space Image Generation](https://mlsanity.com/paper/2605.06421/) (2026)
- [Show the Signal, Hide the Noise: Spectral Forcing for Pixel-Space Diffusion](https://mlsanity.com/paper/2606.15236/) (2026)

## Built on by (most cited first, 1 of 1)

- [Beyond the Manifold Hypothesis: Hybrid Spectral Parameterizations for Flow Matching](https://mlsanity.com/paper/2609.32432/) (2026)

## Abstract (arXiv)

Pixel-space diffusion models directly model image distributions but remain difficult to optimize. Recent methods alleviate this challenge through target reparameterization, while still relying on a fixed clean-image target throughout denoising. Through empirical analysis, we identify a scale-time mismatch: image structures become predictable from coarse to fine as noise decreases, whereas existing models are forced to predict the full image even under high noise, resulting in low-SNR gradients that hinder optimization. To resolve this mismatch, we propose Observation Operator Diffusion, a unified framework that aligns both the supervision trajectory and feature refinement with the intrinsic recovery order of image structures. Specifically, we replace fixed full-image supervision along the standard flow path with a time-indexed observation trajectory that evolves from coarse structures to the full image during denoising. This trajectory is instantiated with a family of Gaussian-Lanczos operators at varying observation scales, yielding a path-consistent training objective. We further introduce GL-CoDA, a decoder that injects scale-specific Gaussian-Lanczos observations across decoding stages for coarse-to-fine feature refinement. Extensive experiments show that the proposed approach converges substantially faster while consistently improving generation quality, achieving an FID of 1.52 on ImageNet-256.