Apple's Normalizing Trajectory Models Generate Images in Four Steps With Exact Likelihood

The problem with few-step generation

Diffusion-based models break sampling into many small Gaussian denoising steps. The authors say this assumption stops holding when generation is compressed into a few coarse transitions.

Existing few-step methods tackle the issue through distillation, consistency training, or adversarial objectives. According to the paper, all of these sacrifice the likelihood framework in the process. NTM is designed to avoid that trade-off.

How NTM works

NTM models each reverse step as an expressive conditional normalizing flow, trained with exact likelihood. The architecture combines two elements:

• shallow invertible blocks within each step;
• a deep parallel predictor across the trajectory.

Together these form an end-to-end network. The authors state it can be trained from scratch or initialized from pretrained flow-matching models, which gives researchers a route to build on existing work.

The exact trajectory likelihood also enables self-distillation. A lightweight denoiser is trained on the score function induced by the model itself, and according to the paper it produces high-quality samples in four steps.

Results and context

On text-to-image benchmarks, NTM "matches or outperforms strong image generation baselines in just four sampling steps", the authors write, while "uniquely retaining exact likelihood over the generative trajectory". The source does not name the specific benchmarks or baselines in its abstract, nor give numerical scores.

The paper is by Jiatao Gu, Tianrong Chen, Ying Shen, David Berthelot, Shuangfei Zhai and Josh Susskind. Gu is affiliated with the University of Pennsylvania and Shen with UIUC, who did the work while at Apple. It was published in October 2026 and is listed under the NeurIPS conference, in the research areas Computer Vision and Methods and Algorithms.

It sits alongside other recent Apple work on likelihood-based generation, such as the May 2026 ICML paper on iterative TARFlow (iTARFlow), which advances Normalizing Flow models as alternatives to diffusion models.

What it means

For researchers, NTM suggests that fast sampling and exact likelihood need not be mutually exclusive. Methods that reach few-step generation by giving up likelihood lose that property, whereas NTM keeps it over the whole generative trajectory, according to the authors. Whether the approach holds up beyond the reported benchmarks, or how it compares in cost with established methods, cannot be judged from the abstract alone.