Apple Machine Learning Research · 10/8/2026, 08:00:00
NTM: Exact Likelihood Four-Step Image Generation via Normalizing Flows
Researchers from UPenn and UIUC introduce Normalizing Trajectory Models (NTM), which use conditional normalizing flows to retain exact likelihood in few-step diffusion sampling. By combining shallow invertible blocks with a deep parallel predictor, NTM achieves state-of-the-art text-to-image results in just four steps while enabling self-distillation through its precise trajectory likelihood.
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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 score function induced by the model itself 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.
- † University of Pennsylvania
- ‡ UIUC
- ** Work done while at Apple