Few-step trajectory distillation aims to learn accurate global updates from dense local supervision along a teacher's sampling trajectory. Existing approaches construct within-step dynamics using specific trajectory parameterizations or discrete interval predictions, tying the learned update to a prescribed temporal structure. We propose \method, which directly learns a continuous trajectory primitive representing cumulative displacement along the teacher trajectory. By supervising finite differences of the primitive with local teacher velocities, \method learns the accumulated motion directly, while obtaining global updates through endpoint differences. This formulation avoids prescribing a temporal basis or fixed query grid and instead learns the temporal evolution of cumulative displacement from local supervision. We further establish a local-to-global error bound to characterize how local regression errors affect full-interval displacement accuracy, and introduce endpoint absorption to eliminate the auxiliary primitive branch while preserving one-network-evaluation inference. Experiments on large-scale text-to-image generation show that \method achieves a T-FID of 20.92 and an HPSv2 score of 28.35 at one NFE, improving both metrics over a trajectory-distillation baseline. After endpoint absorption, it retains comparable performance, achieving a T-FID of 20.86 and an HPSv2 score of 28.33.
Figures & tables
Figure 1: Representing within-step trajectory geometry. A prescribed temporal family or fixed interval grid constrains how the teacher trajectory is represented. PrimFlow directly represents interval integrals as differences of one source-anchored continuous primitive.
Figure 2: Training and deployment of PrimFlow . A single source feature supports continuous primitive queries. Local endpoint differences are matched to teacher velocities, and the learned deployment endpoint is subsequently absorbed into the native prediction head.
Method
Backbone NFE ↓
T-FID ↓
HPSv2 ↑
GenEval ↑
DPG ↑
50-step teacher
50
–
28.81
0.81
85.55
ArcFlow (reproduced)
1
23.55
27.71
0.80
85.36
PrimFlow ( w=512,d=8 )
1
20.92
28.35
0.80
84.98
Table 1: Main quantitative comparison. Distilled models use the same training configuration. The PrimFlow row uses the retained primitive parameterization before absorption. T-FID is measured against the 50-step teacher.
Deployment
Auxiliary params
HPSv2 ↑
T-FID ↓
Primitive retained
25.80M
28.35
20.92
Native head
0
28.33
20.86
Table 2: Endpoint absorption. “Native head” removes the primitive branch after learning its endpoint update; “primitive retained” evaluates the trajectory-trained endpoint directly.
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/.
Efficient text-to-image generation requires both reinforcement-learning (RL)-based reward alignment and few-step distillation, yet these procedures are typically performed sequentially, increasing training cost and risking the loss of reward gains during compression. We take an RL-native perspective: diffusion RL already generates reward-scored finite-step trajectories, whose intermediate states provide distillation supervision. Based on this insight, we propose REST (Reward-Enhanced Scored-Trajectory Distillation), a single-stage co-training framework in which a decoupled student learns from the evolving RL teacher's trajectories without changing teacher optimization. Advantage-Modulated Distillation (AMD) transforms rollout advantages into signed weights, strengthening imitation of preferred trajectories and aligning distillation priorities with task value. The resulting framework is general and lightweight, requires no extra image rollouts, no separate distillation dataset, and no adversarial training. Experiments on compositional generation, visual text rendering, and human-preference alignment demonstrate competitive few-step, CFG-free generation with RAM or DiffusionNFT teachers. With only four sampling steps, REST-RAM achieves a DrawBench PickScore of 23.97, outperforming both the 40-step RAM teacher (23.95) and RTDMD (23.71).
Yuhan Li, Fangao Zeng, Sicong Kang +7
Shanghai Jiao Tong University · Taobao & Tmall group of Alibaba
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.