Abstract

Training-free few-step samplers are often described as nearly quality-lossless under conventional FID/CLIP-style evaluation. It remains unclear whether that conclusion transfers to more realistic and complex generation-quality benchmarks. We first systematize the quality metrics used to evaluate training-free sampling acceleration for diffusion and flow-matching models. We find that representative step-shortening methods often remain nearly lossless under FID/CLIP-class metrics, yet can suffer substantial quality degradation when evaluated with semantic-composition, dense-instruction, and long-text-rendering benchmarks such as GenEval, DPG-Bench, and LongTextBench. Parallel sampling is a notable exception: by retaining the full-step discretization and removing only the solver’s temporal dependency, it can preserve near-lossless quality while accelerating sampling. Building on this observation, we propose ParaLin++, a step-parity parallel sampler that preserves the full-step discretization while accelerating the solver iterations. Experiments across Stable Diffusion-v2, LSUN Church, FLUX.1-dev, and Ming-Flash-Omni 2.0 show that ParaLin++ preserves the full-step Euler quality profile at 2.6×–4.8×, 1.68× on FLUX, and 1.21× on Ming.

The Metric Gap

The decisive axis of a training-free accelerator is the metric that certifies it “quality-lossless”, not the speed lever it uses. Much of the literature stops at distributional and text-alignment proxies, while generation quality is judged on a broader measurable profile:

FID-Lossless ≠ Generation-Quality Preservation

On FLUX.1-dev, 16-step UniPC / DPMSolver++ can appear close to the 30-step Euler reference under FID/CLIP-style metrics, yet degrade sharply on generation-quality benchmarks. ParaLin++ keeps all 30 discrete steps, parallelizes the solver iterations, and preserves the Euler-level quality while being faster:

Table: generation-quality audit on FLUX.1-dev. The same pattern holds across guidance strengths (CFG 0–14) and on Ming-Flash-Omni 2.0, where ParaLin++ keeps the Euler-level profile (GenEval 0.87 vs. 0.88; DPG-Bench 86.99 vs. 86.86; LongTextBench 0.95 vs. 0.95) at 1.21×.

See the Difference

Rows: generation-quality benchmarks (GenEval / DPG-Bench / LongTextBench).
Columns: 30-step Euler, 16-step UniPC, 16-step DPMSolver++, 30-step ParaLin++.

FLUX.1-dev: few-step results keep plausible low-level appearance but break semantics — the pizza gains hole artifacts, the F1 car and boat deform, and the autumn-poster text vanishes; ParaLin++ stays aligned with the Euler reference.

Robust Across Guidance Strengths

Rows: guidance scale (CFG 0 / 3.5 / 7 / 10.5 / 14).
Columns: 30-step Euler, 20-step UniPC, 20-step DPMSolver++, 30-step ParaLin++.

GenEval CFG sweep on FLUX.1-dev: ParaLin++ remains close to the Euler reference while few-step UniPC / DPMSolver++ lose semantic composition as guidance changes.

LongTextBench CFG sweep on FLUX.1-dev, using an English prompt; the reported metric averages the English and Chinese subsets.

DPG-Bench CFG sweep on FLUX.1-dev: as guidance rises, 20-step UniPC / DPMSolver++ drop objects and flatten scene structure, while step-parity ParaLin++ stays aligned with the 30-step Euler reference at every guidance setting.

The Problem with Few-Step Solvers

Step-shortening solvers (DDIM, DPMSolver++, UniPC) buy fewer discrete steps by altering the prompt-conditioned trajectory — and the altered trajectory is exactly what breaks dense-prompt and text fidelity; FID merely fails to reflect this break because it overlooks sample-level semantics. Parallel sampling instead keeps all N discrete steps and removes only the solver's temporal dependency. We call this the step-parity route, and ParaLin++ is a direct realization of this step-parity route.

Our Solution: ParaLin++

ParaLin++ reinterprets sequential sampling as a mixed system of linear and nonlinear equations and solves it in parallel. It combines four components:

Theory: an accumulated error bound relative to the exact sequential trajectory, and convergence of the iteration to the ϱ-nonlinear surrogate system within K ≤ N iterations.

How It Works: The Partially Linear Pipeline

Instead of treating all steps as computationally expensive nonlinear operations, our method linearizes most of the sampling process. As shown in the pipeline below, only a small number of steps (the "Nonlinear Region" ϱ) require full model evaluations. The remaining steps ("Linear Region") are solved with a highly efficient linear solver, dramatically reducing NFE and unleashing parallel efficiency.

Preserving Quality: Intermediate Step Comparison

Our method converges to a high-fidelity image in significantly fewer iterations, demonstrating efficiency without sacrificing quality.

Comparison 1: Expediting DDIM (50 steps).
The rows, from top to bottom, represent DDIM, ParaDiGMS, ParaSolver, ParaLin, and ParaLin++ (the last two shown under their former ParaSolver-Turbo-series names).

Comparison 2: Visual comparison of samplers (50-step DDIM baseline)

Quantitative Results

ParaLin++ substantially reduces wall-clock latency while preserving generation quality. On Stable Diffusion-v2 (classifier guidance w = 7.5) and LSUN Church (5000 samples), it consistently achieves the lowest wall-clock time and iteration counts, with negligible change in FID or CLIP scores, even on a single GPU.

Stable Diffusion-v2

LSUN Church (5000 samples)

Citation

@article{lu2026paralinpp,
  title   = {ParaLin++: Accelerating Parallel Diffusion Integrator
             via Intrinsic Partially Linear Structure},
  author  = {Lu, Jianrong and Zhu, Zhiyu and Liu, Hui and Hou, Junhui},
  journal = {Manuscript under Review},
  year    = {2026}
}