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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 arch","title":"x-Prediction Is All You Need:Training-Free Accelerated Generation via Endpoint Decodability","url":"https://arxiv.org/abs/2607.06114","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.06114v2 Announce Type: replace-cross \nAbstract: 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 $x_0$. 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