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

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.