School of Physical Science and Technology, Beijing University of Posts and Telecommunications, Beijing, China
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
x0 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
E[x0∣xt] under the usual
ℓ2 objective. This yields \textbf{Truncated Jump Sampling} (TJS): stop the ODE at an early-exit time
t∗ and return the decoded
x0. 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.