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

Beyond the Estimate. Wiener-Informed Decoding for Easier Training of Pixel-Space Flow Models. By Ziqiao Wang and one other, from the HPC-AI Lab at the National University of Singapore. Published on the twenty-sixth of October.

Learning velocity fields directly in pixel space is difficult, and it is slow. The authors start from an observation about what can help. Coarse second-order image statistics can ease the task. When frozen Wiener estimates are given to the model, velocity learning improves, and the gains reach beyond the linear predictions those estimates explicitly provide. In other words, the estimate helps by more than its own content would account for. The authors also observe similar gains, complementary ones, from frozen bases and from pixel decoding. Something about the structure of these statistical tools seems to be helping, not only the numbers they output.

Those observations motivate Wiener-informed Decoding, or WiD. The idea is to put statistical knowledge to work twice. Once for direct prediction, as a Wiener estimate would normally be used. And once to organise the computation of the decoder itself. Both are done without modifying the native blocks of the model, so the architecture being trained keeps its own design.

WiD pairs a trainable Wiener prediction path with coefficient interfaces. Those interfaces inject features into the native decoder, and they return its predicted coefficient corrections. Each of these components starts life initialised with data statistics, rather than from scratch. Every introduced parameter, the spectrum and coordinate transforms included, is then trained jointly under the original pixel-space velocity objective. The training target itself does not change: what changes is the scaffolding the decoder works within.

Across model scales and decoder architectures, WiD accelerates training and improves generation quality, at modest parameter overhead. It gives smoother gradient trajectories, and it stays effective when combined with representation alignment. It improves both class-conditional and text-to-image generation, across different resolutions.

The headline number is on ImageNet at two hundred and fifty-six by two hundred and fifty-six pixels. There, PixelDiT-XL with WiD reaches an FID of one point five three after five hundred epochs. That is quality comparable to PixelDiT without it, reached with thirty-seven point five percent fewer training epochs.

Beyond the estimate is meant literally. A statistical denoiser is usually valued for the estimate it produces. Here, its computational structure is put to work as well, and that structure turns out to ease pixel-space training in its own right. The estimate is the starting point, and the paper's point is that the benefit goes beyond it.