# Parametric Trajectory Distillation for Few-Step Video Generation

arXiv: https://arxiv.org/abs/2610.11498 · HTML: https://mlsanity.com/paper/2610.11498/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Video generation, one of 14 directions in Diffusion models.
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Placed in

- Diffusion models / [Video generation](https://mlsanity.com/diffusion/video-generation/)

## Builds on (most cited first, 18 of 18)

- [Wan: Open and Advanced Large-Scale Video Generative Models](https://mlsanity.com/paper/2503.20314/) (2025)
- [V-JEPA 2: Self-Supervised Video Models Enable Understanding, Prediction and Planning](https://mlsanity.com/paper/2506.09985/) (2025)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [VBench-2.0: Advancing Video Generation Benchmark Suite for Intrinsic Faithfulness](https://mlsanity.com/paper/2503.21755/) (2025)
- [GENIE: Higher-Order Denoising Diffusion Solvers](https://mlsanity.com/paper/2210.05475/) (2022)
- [How to build a consistency model: Learning flow maps via self-distillation](https://mlsanity.com/paper/2505.18825/) (2025)
- [Align Your Flow: Scaling Continuous-Time Flow Map Distillation](https://mlsanity.com/paper/2506.14603/) (2025)
- [Large Scale Diffusion Distillation via Score-Regularized Continuous-Time Consistency](https://mlsanity.com/paper/2510.08431/) (2025)
- [Transition Matching Distillation for Fast Video Generation](https://mlsanity.com/paper/2601.09881/) (2026)
- [pi-Flow: Policy-Based Few-Step Generation via Imitation Distillation](https://mlsanity.com/paper/2510.14974/) (2025)
- [SplitMeanFlow: Interval Splitting Consistency in Few-Step Generative Modeling](https://mlsanity.com/paper/2507.16884/) (2025)
- [AnyFlow: Any-Step Video Diffusion Model with On-Policy Flow Map Distillation](https://mlsanity.com/paper/2605.13724/) (2026)
- [Phased DMD: Few-step Distribution Matching Distillation via Score Matching within Subintervals](https://mlsanity.com/paper/2510.27684/) (2025)
- [Terminal Velocity Matching](https://mlsanity.com/paper/2511.19797/) (2025)
- [B'ezierFlow: Learning B'ezier Stochastic Interpolant Schedulers for Few-Step Generation](https://mlsanity.com/paper/2512.13255/) (2025)
- [ViMix-14M: A Curated Multi-Source Video-Text Dataset with Long-Form, High-Quality Captions and Crawl-Free Access](https://mlsanity.com/paper/2511.18382/) (2025)
- [WorldJen: An End-to-End Multi-Dimensional Benchmark for Generative Video Models](https://mlsanity.com/paper/2605.03475/) (2026)
- [Bezier Distillation](https://mlsanity.com/paper/2503.16562/) (2025)

## Abstract (arXiv)

Video diffusion and flow models require many sequential evaluations, making generation computationally expensive. Few-step distillation reduces this cost but poses a capacity allocation problem: a student must match the teacher's iterative generation with far less sequential computation. Existing trajectory methods ask the student to reproduce teacher transitions that are highly curved at high noise, which can exceed its capacity and degrade fine detail. We introduce Parametric Trajectory Distillation (PTD), which lets the student parameterize teacher trajectory segments as polynomials and learn from teacher guidance along its own predicted path. PTD is designed to let the learned curvature adapt to the backbone's predictive capacity, preserving motion and diversity. The curvature head is used only in training; inference keeps the original backbone architecture. On Wan2.1-14B, four-step PTD sets a new state of the art for trajectory distillation, significantly improving dynamic quality and naturalness over PDD, the best-performing trajectory-only method on this model, under the same training setting. On the 33B audio-video MiniMax-H3, LoRA-trained PTD significantly improves diversity and naturalness over the state-of-the-art LightX2V Turbo. Blinded human votes give PTD 55.1% and 63.4% preference shares against PDD and LightX2V Turbo. Project page: https://alan-lanfeng.github.io/PTD/.