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Normalizing Trajectory Models

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Flow matching distillation · 0 citations (OpenAlex)

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Proposes Normalizing Trajectory Models (NTM), which model each reverse diffusion step as a conditional normalizing flow (invertible transporter plus Gaussian predictor) for exact-likelihood few-step generation, trained from scratch or finetuned from FLUX.2-klein.

Problem

Few-step diffusion/flow generation breaks the Gaussian reverse-step assumption, while existing few-step methods (distillation, consistency, adversarial) give up tractable likelihood.

Approach

Model p(x_s|x_t) as a conditional normalizing flow: a shared invertible same-dimensional autoregressive transporter maps x to a latent u-space where a Gaussian predictor applies, giving exact NLL via change of variables; add trajectory-level covariance-weighted score denoising and a distilled single-pass denoiser.

Key results

• NTM trained from scratch at 256x256 achieves 0.82 GenEval and 79.64 DPG-Bench in 4 steps, vs STARFlow 0.56 GenEval.
• Class-conditional ImageNet: NTM reaches 3.83 FID with 4 steps and 2.80 FID with 16 steps, vs STARFlow (FAE) 2.67 FID with 256 AR steps.
• Finetuned 512x512 NTM reaches 0.76 GenEval and 83.38 DPG-Bench; learned denoiser gives ~9x speedup (1.88 vs 0.20 img/s) over trajectory score denoising.

Surprising findings

• With T=1 NTM produces severely degraded outputs, showing single-step exact-likelihood generation remains hard.
• Finetuning with the NLL objective alone diverges without the mean-alignment auxiliary loss.

Limitations

• T=1 single-step generation degrades severely due to limited transporter capacity.
• Position and attribute-binding sub-tasks remain challenging in the finetuned setting.
• Trained on an internal dataset of ~70M pairs, limiting reproducibility.

Experimental setup

Datasets: ImageNet CC12M internal text-image dataset (~70M pairs)

Benchmarks: GenEval DPG-Bench ImageNet 256x256 FID

Metrics: GenEval overall score DPG-Bench accuracy FID LPIPS images per second

Baselines: STARFlow SDXL PixArt-alpha SD3-Medium FLUX.1-dev Janus-Pro-7B HiDream-I1-Full Seedream 3.0 Qwen-Image Nucleus-Image FLUX.2-klein

Builds on: TarFlow STARFlow flow matching NFM classifier-free guidance

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