Normalizing Trajectory Models

TL;DR

Normalizing Trajectory Models (NTM) enable efficient, high-quality trajectory modeling with exact likelihood training, reducing diffusion steps to four while maintaining or surpassing existing image generation benchmarks.

Contribution

NTM introduces a novel approach combining normalizing flows with trajectory modeling, enabling exact likelihood training and effective self-distillation for fast image synthesis.

Findings

NTM matches or outperforms strong baselines in four steps.

NTM retains exact likelihood over the generative trajectory.

Self-distillation with a lightweight denoiser yields high-quality samples.

Abstract

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.