x-Prediction Is All You Need:Training-Free Accelerated Generation via Endpoint Decodability

2026-07-07

AI Summary

This work addresses the inefficiency of ODE-based samplers in diffusion and flow-matching models, which typically require tens to hundreds of neural network evaluations per sample. While existing acceleration methods often rely on retraining or distillation, the authors propose Truncated Jump Sampling (TJS), a training-free early-exit strategy. Building on the x-prediction perspective and leveraging the information exposure of intermediate states about the initial sample \(x_0\) along affine probability paths, they formalize the novel concept of “endpoint decodability” and prove its equivalence to minimum mean squared error estimation. TJS exploits this insight to significantly accelerate sampling without altering model architecture or requiring retraining. Experiments demonstrate that TJS reduces the number of function evaluations (NFE) by 20%–70% across SDXL, SD3.5M, Z-Image-Turbo, and multiple class-conditional benchmarks while preserving near-original generation quality.

Abstract

Diffusion and flow matching models generate high-quality samples, but their ODE samplers often need tens to hundreds of neural function evaluations (NFEs). This remains a practical challenge for released checkpoints, since many accelerators require additional design choices and training cost through retraining, distillation, or trajectory redesign. We investigate a different route based on $x$-prediction. During sampling, standard affine probability paths already expose $x_0$ information: an intermediate state and its path velocity determine a principled estimate of the clean sample. We formalize this property as \textbf{endpoint decodability} and show that the decoder is the minimum-MSE estimator $\mathbb{E}[x_0\mid x_t]$ under the usual $\ell_2$ objective. This yields \textbf{Truncated Jump Sampling} (TJS): stop the ODE at an early-exit time $t^*$ and return the decoded $x_0$. TJS requires no retraining, distillation, or architecture change. Across SDXL, SD3.5M, Z-Image-Turbo, and three class-conditional benchmarks, it reduces NFEs by 20--70\% with near-matched quality. The analysis also shows why endpoint prediction can work without straightening the trajectory, providing inference acceleration without trajectory redesign.

Problem

• diffusion models
• flow matching
• neural function evaluations
• inference acceleration
• sampling efficiency

Innovation

• endpoint decodability
• Truncated Jump Sampling
• training-free acceleration
• diffusion models
• flow matching