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

arXiv: https://arxiv.org/abs/2607.06114 · HTML: https://mlsanity.com/paper/2607.06114/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 9 of its 46 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)
- Efficient LLM inference and serving / [Diffusion LLM and MoE inference](https://mlsanity.com/inference/diffusion-llm-and-moe-inference/)

## Builds on (most cited first, 9 of 9)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Z-Image: An Efficient Image Generation Foundation Model with Single-Stream Diffusion Transformer](https://mlsanity.com/paper/2511.22699/) (2025)
- [Trajectory Consistency Distillation: Improved Latent Consistency Distillation by Semi-Linear Consistency Function with Trajectory Mapping](https://mlsanity.com/paper/2402.19159/) (2024)
- [A Geometric Perspective on Diffusion Models](https://mlsanity.com/paper/2305.19947/) (2023)
- [Back to Basics: Let Denoising Generative Models Denoise](https://mlsanity.com/paper/2511.13720/) (2025)
- [Dense-Jump Flow Matching with Non-Uniform Time Scheduling for Robotic Policies: Mitigating Multi-Step Inference Degradation](https://mlsanity.com/paper/2509.13574/) (2025)

## Built on by (most cited first, 1 of 1)

- [ELF-REG: Scaling Continuous Diffusion Language Models to Reasoning Tasks](https://mlsanity.com/paper/2609.29102/) (2026)

## Abstract (arXiv)

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 endpoint decodability and show that the decoder is the minimum-MSE estimator mathbbE[x0mid xt] under the usual ℓ2 objective. This yields 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.