# MGPO: Manifold-Guided Diffusion Alignment for Task-Aware Dataset Distillation

arXiv: https://arxiv.org/abs/2610.05252 · HTML: https://mlsanity.com/paper/2610.05252/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 31 of its 41 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- LLM alignment / RLHF / preference optimisation / [Diffusion and multimodal model alignment](https://mlsanity.com/alignment/diffusion-and-multimodal-model-alignment/)

## Builds on (most cited first, 30 of 31)

- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [Dataset Condensation with Gradient Matching](https://mlsanity.com/paper/2006.05929/) (2020)
- [Dataset Distillation by Matching Training Trajectories](https://mlsanity.com/paper/2203.11932/) (2022)
- [DanceGRPO: Unleashing GRPO on Visual Generation](https://mlsanity.com/paper/2505.07818/) (2025)
- [Dataset Condensation with Distribution Matching](https://mlsanity.com/paper/2110.04181/) (2021)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [Dataset Condensation via Efficient Synthetic-Data Parameterization](https://mlsanity.com/paper/2205.14959/) (2022)
- [MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE](https://mlsanity.com/paper/2507.21802/) (2025)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [Squeeze, Recover and Relabel: Dataset Condensation at ImageNet Scale From A New Perspective](https://mlsanity.com/paper/2306.13092/) (2023)
- [On the Diversity and Realism of Distilled Dataset: An Efficient Dataset Distillation Paradigm](https://mlsanity.com/paper/2312.03526/) (2023)
- [DiffFit: Unlocking Transferability of Large Diffusion Models via Simple Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2304.06648/) (2023)
- [Efficient Dataset Distillation via Minimax Diffusion](https://mlsanity.com/paper/2311.15529/) (2023)
- [Gradient Guidance for Diffusion Models: An Optimization Perspective](https://mlsanity.com/paper/2404.14743/) (2024)
- [BranchGRPO: Stable and Efficient GRPO with Structured Branching in Diffusion Models](https://mlsanity.com/paper/2509.06040/) (2025)
- [Diffusion Models as Cartoonists: The Curious Case of High Density Regions](https://mlsanity.com/paper/2411.01293/) (2024)
- [Dataset Distillation via Vision-Language Category Prototype](https://mlsanity.com/paper/2506.23580/) (2025)
- [Taming Diffusion for Dataset Distillation with High Representativeness](https://mlsanity.com/paper/2505.18399/) (2025)
- [CaO2: Rectifying Inconsistencies in Diffusion-Based Dataset Distillation](https://mlsanity.com/paper/2506.22637/) (2025)
- [Estimating the reach of a manifold via its convexity defect function](https://mlsanity.com/paper/2001.08006/) (2020)

## Abstract (arXiv)

Diffusion-based dataset distillation (DD) suffers from a fundamental objective mismatch: likelihood-driven diffusion models prioritize density approximation over the discriminative decision boundaries required for downstream tasks. Beyond semantic mismatch, relying solely on density also leads to geometric coverage loss, where generated samples collapse into a few high-density modes and fail to cover the manifold's structural diversity. We propose Manifold-Guided Policy Optimization (MGPO), which reformulates DD as a multi-objective reinforcement learning problem and achieves Dual-Space Alignment via a pixel-space discriminative reward and a latent-space geometric reward guided by a class-wise Minimum Spanning Tree (MST). The discriminative reward enforces class separability, while the MST-based geometric reward encourages generated latents to cover a sparse geometric skeleton of each class, jointly addressing both failure modes. We further provide an idealized analysis that motivates the MST-based reward, including a Hausdorff approximation bound and a subsampling bound independent of the dataset size. The reward-modular design extends to structured tasks such as object detection and segmentation by substituting the frozen task reward model. Extensive experiments show MGPO consistently outperforms existing methods, including a +8.0% mIoU gain on segmentation under low-budget settings.