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One-Step Offline Distillation of Diffusion-based Models via Koopman Modeling

NeurIPS 2025 · Image generation › Fast diffusion sampling · approach: Training-free diffusion acceleration · 0 citations (OpenAlex)

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Proposes KDM, an offline one-step diffusion distillation method that encodes noise and clean samples, applies a learned finite-dimensional Koopman linear operator in latent space, and decodes the result.

Problem

Iterative diffusion sampling is computationally expensive; offline distillation (student trained only on precomputed teacher noise-image pairs) lags online methods in quality, and needs a principled way to capture teacher dynamics in one step.

Approach

Model the noise-to-data mapping of a pretrained diffusion teacher as a single linear evolution in a learned embedding space via Koopman operator theory (encoder, linear Koopman layer, decoder), with reconstruction, latent-consistency, prediction and adversarial losses; theoretically argues a finite-dimensional Koopman representation exists for analytic maps and that latent proximity implies semant

Key results

• On unconditional CIFAR-10, KDM (EDM teacher) reaches FID 4.65 with 1 NFE versus GET's 6.91 and IMM's 4.81 among offline methods.
• On class-conditional CIFAR-10, KDM-F reaches FID 3.24 versus GET's 6.25 (about 40% improvement).
• KDM is about 4x faster per training iteration and over 8x faster sampling than GET at the same parameter count (62M).

Measured effects reported in the paper

Surprising findings

• Smaller Koopman matrices generalized better (FID 5.08 at size 1024 vs 9.41 at 9216), contrary to the trend that larger parameter counts help elsewhere.
• In a human study, evaluators preferred the student's collages 55% of the time versus 45% for the EDM teacher.

Limitations

• Gap to online distillation methods and to the teacher remains (e.g., FID 6.54 vs 2.47 on FFHQ), with about 2.5x FID degradation relative to EDM.
• Outlier samples arise from Gaussian prior tails and decision boundaries, reflecting error-prone high-uncertainty regions.
• Evaluated only on small 32x32 and 64x64 resolution datasets; ImageNet and text-to-image not tested due to compute.

Experimental setup

Datasets: CIFAR-10 FFHQ 64x64 AFHQv2 64x64 Checkerboard

Benchmarks: CIFAR-10 unconditional CIFAR-10 class-conditional FFHQ 64x64 AFHQv2 64x64

Metrics: FID IS LPIPS MSE human preference ratio

Baselines: GET IMM 2-rf++ w/o pre-train PD DFNO iCD-EDM CTM ECM StyleGAN-XL BigGAN StyleGAN2-ADA Guided Distillation

Builds on: EDM GET Koopman operator theory LPIPS

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