# DASH: Dual-Branch Score Distillation for Guidance-Calibrated Compact Diffusion Models

arXiv: https://arxiv.org/abs/2606.00798 · HTML: https://mlsanity.com/paper/2606.00798/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 36 of its 41 references that are in the map.
- First posted on arXiv 30 May 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [On Distillation of Guided Diffusion Models](https://mlsanity.com/paper/2210.03142/) (2022)
- [Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion](https://mlsanity.com/paper/2310.02279/) (2023)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [DoReMi: Optimizing Data Mixtures Speeds Up Language Model Pretraining](https://mlsanity.com/paper/2305.10429/) (2023)
- [A Downsampled Variant of ImageNet as an Alternative to the CIFAR datasets](https://mlsanity.com/paper/1707.08819/) (2017)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Perception Prioritized Training of Diffusion Models](https://mlsanity.com/paper/2204.00227/) (2022)
- [Guiding a Diffusion Model with a Bad Version of Itself](https://mlsanity.com/paper/2406.02507/) (2024)
- [Applying Guidance in a Limited Interval Improves Sample and Distribution Quality in Diffusion Models](https://mlsanity.com/paper/2404.07724/) (2024)
- [Efficient Diffusion Training via Min-SNR Weighting Strategy](https://mlsanity.com/paper/2303.09556/) (2023)
- [SnapFusion: Text-to-Image Diffusion Model on Mobile Devices within Two Seconds](https://mlsanity.com/paper/2306.00980/) (2023)
- [Structural Pruning for Diffusion Models](https://mlsanity.com/paper/2305.10924/) (2023)
- [RegMix: Data Mixture as Regression for Language Model Pre-training](https://mlsanity.com/paper/2407.01492/) (2024)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)

## Built on by (most cited first, 1 of 1)

- [Closing the Null Space: Guidance-Aware Quantization for Classifier-Free Diffusion](https://mlsanity.com/paper/2607.08241/) (2026)

## Abstract (arXiv)

Parameter compression of class-conditional diffusion models exposes a structural limitation in output-level distillation: supervising only the guided output leaves the two score branches non-identifiable, so the classifier-free guidance gap is not determined in the student. The zero-loss set admits degenerate solutions in which both branches collapse toward identical predictions, and guidance loses its effect at inference despite low training loss. For each fixed input the objective is exactly flat in a branch-output direction at every residual value, so the ambiguity is a property of the output-level objective rather than a poor local minimum. This paper introduces DASH, which supervises the conditional and unconditional branches independently. An anchor term regularises the conditional prediction toward ground-truth noise, and the teacher's final learned per-timestep curriculum transfers into the student as a frozen prior. Across CIFAR-10, CIFAR-100, and class-conditional ImageNet-64, a more than 5x compressed student stays within four FID points of its teacher and recovers at least 89% of the teacher's guidance-gap magnitude, where no other two-branch baseline with defined calibration exceeds 82%. Ablation isolates unconditional supervision as the term that separates this formulation from output-level distillation. The account is quantitative: the null space fixes the ratio between a composite student's two branch errors, and the measured ratios approximately match that prediction on all three datasets.