normalizing-trajectory-models

# Normalizing Trajectory Models (NTM) ## Core Concept NTM reframes diffusion sampling: each reverse step is a conditional normalizing flow with **exact likelihood** training, unlike adversarial/consistency methods that lose likelihood. Architecture: shallow invertible blocks per-step + deep parallel predictor across trajectory. ## Key Architectural Components ### 1. Invertible Blocks Per-Step - Each denoising step uses shallow invertible transformations - Maintains bijective mapping between noisy and clean states - Enables exact log-likelihood computation at every step ### 2. Parallel Trajectory Predictor - Deep network predicts across the entire trajectory in parallel - Captures long-range dependencies between time steps - Trainable from scratch or initialized from pretrained flow-matching models ### 3. Self-Distillation Pipeline - Train lightweight denoiser on the model's own score function - Produces high-quality samples in 4 steps - The exact trajectory likelihood enables this without distillation targets ## Training Workflow ``` 1. Initialize: from scratch OR pretrained flow-matching model 2. Forward pass: compute trajectory with invertible blocks + parallel predictor 3. Loss: exact trajectory likelihood (log p(x_0|x_t)) 4. Self-distill: train lightweight 4-step denoiser on model's score 5. Sample: run 4-step reverse process ``` ## When to Use NTM - Need few-step (2-4 steps) generation with quality matching 50+ step diffusion - Require exact likelihood (e.g., for model comparison, anomaly detection) - Want self-distillation without sacrificing likelihood framework - Building on top of pretrained flow-matching or diffusion models ## Key Advantages vs Alternatives | Method | Steps | Likelihood | Quality | |--------|-------|------------|---------| | Standard Diffusion | 50-1000 | Exact | High | | Consistency Models | 1-4 | Lost | High | | Adversarial Few-Step | 1-4 | Lost | High | | **NTM** | **4** | **Exact** | **High** | ## References - arXiv: 2605.08078 - "Normalizing Trajectory Models" by Jiatao Gu et al.