Beyond the Estimate: Wiener-Informed Decoding for Easier Training of Pixel-Space Flow Models

Flow-based generation in high-dimensional pixel spaces is difficult because velocity prediction requires modeling high-dimensional noise, even when data has strong low-rank structure. We present Asymmetric Flow Modeling (AsymFlow), a rank-asymmetric velocity parameterization that restricts noise prediction to a low-rank subspace while keeping data prediction full-dimensional. From this asymmetric prediction, AsymFlow analytically recovers the full-dimensional velocity, leaving the network architecture and the standard flow-matching training and sampling procedures unchanged. On ImageNet 256$\times$256, AsymFlow achieves a leading 1.57 FID, outperforming prior DiT/JiT-like pixel diffusion models by a large margin. AsymFlow also provides the first-ever route for finetuning pretrained latent flow models into pixel-space models: aligning the low-rank pixel subspace to the latent space gives a seamless initialization that preserves the latent model's high-level semantics and structure, so finetuning mainly improves low-level mismatches rather than relearning pixel generation. We show that the pixel AsymFlow model finetuned from FLUX.2 klein 9B establishes a new state of the art for pixel-space text-to-image generation, beating its latent base on HPSv3, DPG-Bench, and GenEval while qualitatively showing substantially improved visual realism.

While recent Flow Matching models avoid the reconstruction bottlenecks of latent autoencoders by operating directly in pixel space, the raw pixel manifold provides little explicit semantic organization, making target-specific transport directions difficult for a shared finite-capacity vector field to distinguish. When different transport requirements are locally entangled in this way, their learning signals can interfere and hinder optimization, a phenomenon we refer to as trajectory conflict. To alleviate trajectory conflict while preserving direct generation in pixel space, we propose Waypoint Diffusion Transformers (WiT), which introduces explicit semantic routing into pixel-space generation. WiT structures pixel-space prediction through compact semantic waypoints projected from pre-trained vision representations, providing a semantically organized intermediate representation that complements direct pixel prediction. During ODE integration, a lightweight Waypoints Predictor dynamically infers the semantic waypoint from the current noisy state, and the predicted waypoint continuously conditions the primary Pixel Space Generator through our Just-Pixel AdaLN mechanism. This spatially varying semantic modulation reorganizes the finite-capacity learning problem and helps the model preserve target-specific transport directions while retaining generation entirely in pixel space. Experiments on ImageNet 2012 demonstrate consistent improvements over strong pixel-space baselines across model scales, with WiT-H/16 achieving an FID of 1.79. Code will be released at https://hainuo-wang.github.io/WiT.

Co-denoising pretrained representations such as DINO can substantially improve the training speed and quality of flow matching models, but it introduces a second denoising trajectory and requires carefully designed schedules. We propose a simpler alternative: predict the pretrained representation directly, then condition the model on its own prediction. This removes the need for a second ODE and any representation-specific denoising schedules, while retaining the benefits of representation guidance. Our approach converges substantially faster and achieves better generation quality as measured by FID score. On ImageNet, it outperforms the state of the art in latent space at 2x fewer epochs than prior methods; in pixel space, it improves FID over comparable prior methods by more than 20%. These results support a simple principle: do not denoise what you can predict. Our code is openly available at https://github.com/arijit-hub/dino_forcing.