Normalizing Trajectory Models
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| Authors | Jiatao Gu et al. |
| Year | 2026 |
| HF Upvotes | 2 |
| arXiv | 2605.08078 |
| Download | |
| HF Page | View on Hugging Face |
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.
Engineering Breakdown
Plain English
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Key Engineering Insight
NTM achieves fast generation without sacrificing the likelihood framework by making each denoising step invertible and trainable as a normalizing flow. This means you get exact log-likelihood gradients for training while still hitting few-step generation targets — a capability prior fast-sampling methods couldn't offer because they switched to adversarial or distillation objectives that lose likelihood guarantees.
Why It Matters for Engineers
For production systems, this matters because likelihood-based training is more stable and predictable than adversarial objectives, and having exact likelihood enables better uncertainty quantification and model debugging. Fast few-step generation has been a key bottleneck in deploying diffusion models at scale; NTM removes the traditional trade-off between speed and training stability, making faster models easier to ship reliably.
Research Context
Prior work on fast diffusion models relied on distillation (copying from slow models) or adversarial training (which often destabilizes), both abandoning the likelihood framework that made diffusion models theoretically clean. NTM advances the field by showing you can have both exact likelihoods and few-step inference by reformulating the trajectory as a sequence of invertible transformations, and further enables self-distillation where a model can improve itself using its own likelihood scores.
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