Back to Devoured - May 12, 2026

DEVOURED

Trajectory Models for Few-Step Diffusion

AI researchdiffusionimage-generation arXiv

Apple researchers reduce diffusion image generation to four steps without discarding the likelihood framework that consistency training and distillation methods abandon

What: Jiatao Gu, Ying Shen, David Berthelot, Shuangfei Zhai, and Josh Susskind introduced Normalizing Trajectory Models (NTM), which models each reverse diffusion step as a conditional normalizing flow. The approach achieves competitive text-to-image quality in four sampling steps while maintaining exact trajectory likelihood. NTM supports self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. Submitted to arXiv May 8, 2026, revised May 12, 2026.

Why it matters: Few-step diffusion has traditionally required abandoning the likelihood framework for speed gains through distillation, consistency training, or adversarial objectives. NTM suggests the trade-off is unnecessary: expressive conditional flows can compress sampling from dozens to four steps while preserving the mathematical foundations that enable techniques like self-distillation and likelihood-based training.

Deep dive

Standard diffusion models decompose sampling into many small Gaussian denoising steps, an assumption that breaks down when generation is compressed to a few coarse transitions
Existing few-step methods (distillation, consistency training, adversarial objectives) sacrifice the likelihood framework to achieve speed
Normalizing Trajectory Models (NTM) models each reverse diffusion step as an expressive conditional normalizing flow with exact likelihood training
Architecture combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory
The network is trainable from scratch or initializable from pretrained flow-matching models
Exact trajectory likelihood enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples
On text-to-image benchmarks, NTM matches or outperforms strong baselines in four sampling steps
NTM uniquely retains exact likelihood over the generative trajectory while achieving few-step performance
Paper is 25 pages with 10 figures; revised version corrected typos and citations

Decoder

Normalizing flow: A class of generative models that transforms a simple distribution into a complex one through a sequence of invertible functions, allowing exact likelihood computation
Flow-matching: A training framework for generative models that learns to map noise to data by matching velocity fields along continuous trajectories
Self-distillation: Training a smaller or faster model using samples and scores from the original model itself rather than from a separate teacher model

Original article

Normalizing Trajectory Models

Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation, consistency training, or adversarial objectives, but sacrifice the likelihood framework in the process. We introduce Normalizing Trajectory Models (NTM), which models each reverse step as an expressive conditional normalizing flow with exact likelihood training. Architecturally, NTM combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network trainable from scratch or initializable from pretrained flow-matching models. Its exact trajectory likelihood further enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. On text-to-image benchmarks, NTM matches or outperforms strong image generation baselines in just four sampling steps while uniquely retaining exact likelihood over the generative trajectory.

Explore all 40 articles in today's digest