Flow-WLS: Savitzky-Golay regularized solver fixes high-order sampler collapse, clean 10-step DiT generation in 11s
YakovSava · reddit · 2026-10-13
A Reddit research release investigating why high-order diffusion samplers (DPM-Solver++, Adams-Bashforth order 4+) collapse on Flow Matching DiT models, with a new training-free solver Flow-WLS achieving clean, anatomically coherent 10-step generations in 11s on a consumer RTX 5060.
Why high-order samplers break:
- Lagrange polynomial trap: classical multistep methods fit exact interpolating polynomials; at order 5–6 the alternating-sign weights amplify high-frequency network errors 20x+, dropping SSIM to 0.1341 (pure noise).
- EDM vs Flow Matching coordinate mismatch: borrowing EDM transforms (y = x/α) blows up latent variance 10,000x on flow models where σ→1 and α→10⁻⁴, causing 90% white clipping. Integrate directly in canonical velocity space dx/dt = v.
The fix: Flow-WLS fits a rigidly regularized degree-2 parabola across 3–8 history steps via Weighted Least Squares with exponential memory decay (γ=0.85). Degree-2 curves can't oscillate (zero Runge phenomenon), and weight norms decay with history (Σ|wᵢ| = 0.066 vs classical AB's 0.54) — history becomes a Savitzky-Golay smoothing filter without slowing inference.
Benchmarks (Anima DiT 720×1280, RTX 5060): 10-step flowwls8 hits SSIM 0.8003 with zero artifacts; 30-step 0.7541 beats built-in unipc (0.7459); classical order-6 collapses to noise (0.1341); 15 steps yields flawless hand/finger anatomy.
Try it: open-source with Zenodo DOI (10.5281/zenodo.23337579); drop the ComfyUI custom node into customnodes and select flowwls8/5 in a standard KSampler.
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