# Apple — Normalizing Trajectory Models

- Company: Apple (apple.com)
- Announced: 2026-10-08
- Category: research-paper
- Coverage: not counted
- Announcement: yes
- Group: announcements
- Source: https://machinelearning.apple.com/research/normalizing-trajectory-models
- Record: https://forck.live/items/16806-normalizing-trajectory-models
- Subject: Machine Learning Research

Apple researchers introduced Normalizing Trajectory Models (NTM), which models each reverse diffusion step as an expressive conditional normalizing flow with exact likelihood training. The architecture combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network that can be trained from scratch or initialized from pretrained flow-matching models. On text-to-image benchmarks, NTM matches or outperforms strong image generation baselines in just four sampling steps while retaining exact likelihood over the generative trajectory.

## Evidence

Verbatim from https://machinelearning.apple.com/research/normalizing-trajectory-models:

> 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.

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