Normalizing Trajectory Models
For generative modeling practitioners, NTM provides a method that combines few-step generation with exact likelihood, addressing a key limitation of existing few-step diffusion methods.
NTM introduces a diffusion-like generative model where each reverse step is a normalizing flow, enabling exact likelihood training and high-quality few-step generation. On text-to-image tasks, it matches or outperforms strong baselines in four sampling steps.
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.