# Guiding Diffusion with Deep Geometric Moments: Balancing Fidelity and Variation

arXiv: https://arxiv.org/abs/2505.12486 · HTML: https://mlsanity.com/paper/2505.12486/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 35 of its 37 references that are in the map.
- First posted on arXiv 18 May 2025.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 30 of 35)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [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)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [IP-Adapter: Text Compatible Image Prompt Adapter for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2308.06721/) (2023)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Deep ViT Features as Dense Visual Descriptors](https://mlsanity.com/paper/2112.05814/) (2021)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [A Survey on Diffusion Models for Inverse Problems](https://mlsanity.com/paper/2410.00083/) (2024)
- [Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing](https://mlsanity.com/paper/2407.01521/) (2024)
- [Manifold Preserving Guided Diffusion](https://mlsanity.com/paper/2311.16424/) (2023)
- [TFG: Unified Training-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2409.15761/) (2024)
- [No Training, No Problem: Rethinking Classifier-Free Guidance for Diffusion Models](https://mlsanity.com/paper/2407.02687/) (2024)
- [Readout Guidance: Learning Control from Diffusion Features](https://mlsanity.com/paper/2312.02150/) (2023)
- [λ-ECLIPSE: Multi-Concept Personalized Text-to-Image Diffusion Models by Leveraging CLIP Latent Space](https://mlsanity.com/paper/2402.05195/) (2024)
- [Steering Rectified Flow Models in the Vector Field for Controlled Image Generation](https://mlsanity.com/paper/2412.00100/) (2024)
- [Understanding and Improving Training-free Loss-based Diffusion Guidance](https://mlsanity.com/paper/2403.12404/) (2024)
- [ECLIPSE: A Resource-Efficient Text-to-Image Prior for Image Generations](https://mlsanity.com/paper/2312.04655/) (2023)
- [Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models](https://mlsanity.com/paper/2502.11420/) (2025)
- [Rethinking Diffusion Posterior Sampling: From Conditional Score Estimator to Maximizing a Posterior](https://mlsanity.com/paper/2501.18913/) (2025)
- [Distilling Diversity and Control in Diffusion Models](https://mlsanity.com/paper/2503.10637/) (2025)

## Abstract (arXiv)

Text-to-image generation models have achieved remarkable capabilities in synthesizing images, but often struggle to provide fine-grained control over the output. Existing guidance approaches, such as segmentation maps and depth maps, introduce spatial rigidity that restricts the inherent diversity of diffusion models. In this work, we introduce Deep Geometric Moments (DGM) as a novel form of guidance that encapsulates the subject's visual features and nuances through a learned geometric prior. DGMs focus specifically on the subject itself compared to DINO or CLIP features, which suffer from overemphasis on global image features or semantics. Unlike ResNets, which are sensitive to pixel-wise perturbations, DGMs rely on robust geometric moments. Our experiments demonstrate that DGM effectively balance control and diversity in diffusion-based image generation, allowing a flexible control mechanism for steering the diffusion process.