# Norm-guided latent space exploration for text-to-image generation

arXiv: https://arxiv.org/abs/2306.08687 · HTML: https://mlsanity.com/paper/2306.08687/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 59 of its 76 references that are in the map.
- First posted on arXiv 14 Jun 2023.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 30 of 59)

- [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)
- [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)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Learning to Prompt for Vision-Language Models](https://mlsanity.com/paper/2109.01134/) (2021)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [Encoding in Style: a StyleGAN Encoder for Image-to-Image Translation](https://mlsanity.com/paper/2008.00951/) (2020)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2301.13826/) (2023)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Image2StyleGAN: How to Embed Images Into the StyleGAN Latent Space?](https://mlsanity.com/paper/1904.03189/) (2019)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Make-A-Scene: Scene-Based Text-to-Image Generation with Human Priors](https://mlsanity.com/paper/2203.13131/) (2022)
- [MaxViT: Multi-Axis Vision Transformer](https://mlsanity.com/paper/2204.01697/) (2022)
- [Tip-Adapter: Training-free CLIP-Adapter for Better Vision-Language Modeling](https://mlsanity.com/paper/2111.03930/) (2021)
- [In-Domain GAN Inversion for Real Image Editing](https://mlsanity.com/paper/2004.00049/) (2020)

## Built on by (most cited first, 30 of 43)

- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [Lightning-Fast Image Inversion and Editing for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2312.12540/) (2023)
- [AID: Attention Interpolation of Text-to-Image Diffusion](https://mlsanity.com/paper/2403.17924/) (2024)
- [ImageRAG: Dynamic Image Retrieval for Reference-Guided Image Generation](https://mlsanity.com/paper/2502.09411/) (2025)
- [FreeMorph: Tuning-Free Generalized Image Morphing with Diffusion Model](https://mlsanity.com/paper/2507.01953/) (2025)
- [DASH: Detection and Assessment of Systematic Hallucinations of VLMs](https://mlsanity.com/paper/2503.23573/) (2025)
- [TKG-DM: Training-free Chroma Key Content Generation Diffusion Model](https://mlsanity.com/paper/2411.15580/) (2024)
- [It's Never Too Late: Noise Optimization for Collapse Recovery in Trained Diffusion Models](https://mlsanity.com/paper/2601.00090/) (2025)
- [Memories of Forgotten Concepts](https://mlsanity.com/paper/2412.00782/) (2024)
- [ORIGEN: Zero-Shot 3D Orientation Grounding in Text-to-Image Generation](https://mlsanity.com/paper/2503.22194/) (2025)
- [Manipulating Embeddings of Stable Diffusion Prompts](https://mlsanity.com/paper/2308.12059/) (2023)
- [Synthetic Shifts to Initial Seed Vector Exposes the Brittle Nature of Latent-Based Diffusion Models](https://mlsanity.com/paper/2312.11473/) (2023)
- [Diverse Diffusion: Enhancing Image Diversity in Text-to-Image Generation](https://mlsanity.com/paper/2310.12583/) (2023)
- [Linear combinations of latents in generative models: subspaces and beyond](https://mlsanity.com/paper/2408.08558/) (2024)
- [Adjusting Initial Noise to Mitigate Memorization in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2510.08625/) (2025)
- [Textured 3D Regenerative Morphing with 3D Diffusion Prior](https://mlsanity.com/paper/2502.14316/) (2025)
- [What's Inside Your Diffusion Model? A Score-Based Riemannian Metric to Explore the Data Manifold](https://mlsanity.com/paper/2505.11128/) (2025)
- [Image Interpolation with Score-based Riemannian Metrics of Diffusion Models](https://mlsanity.com/paper/2504.20288/) (2025)
- [S2ST: Image-to-Image Translation in the Seed Space of Latent Diffusion](https://mlsanity.com/paper/2312.00116/) (2023)
- [Optimizing Resource Consumption in Diffusion Models through Hallucination Early Detection](https://mlsanity.com/paper/2409.10597/) (2024)
- [Repurposing Marigold for Zero-Shot Metric Depth Estimation via Defocus Blur Cues](https://mlsanity.com/paper/2505.17358/) (2025)
- [Moment- and Power-Spectrum-Based Gaussianity Regularization for Text-to-Image Models](https://mlsanity.com/paper/2509.07027/) (2025)
- [Be Tangential to Manifold: Discovering Riemannian Metric for Diffusion Models](https://mlsanity.com/paper/2510.05509/) (2025)
- [Vibe Spaces for Creatively Connecting and Expressing Visual Concepts](https://mlsanity.com/paper/2512.14884/) (2025)
- [Beyond Flat Text: Dual Self-inherited Guidance for Visual Text Generation](https://mlsanity.com/paper/2501.05892/) (2025)
- [Geometric Consistency Refinement for Single Image Novel View Synthesis via Test-Time Adaptation of Diffusion Models](https://mlsanity.com/paper/2504.08348/) (2025)
- [T2IBias: Uncovering Societal Bias Encoded in the Latent Space of Text-to-Image Generative Models](https://mlsanity.com/paper/2511.10089/) (2025)
- [3D-Consistent Multi-View Editing by Correspondence Guidance](https://mlsanity.com/paper/2511.22228/) (2025)
- [Trajectory Stitching for Solving Inverse Problems with Flow-Based Models](https://mlsanity.com/paper/2602.08538/) (2026)
- [Gradient Preconditioning for Efficient and Reliable Reward-Guided Generation](https://mlsanity.com/paper/2602.08646/) (2026)

## Abstract (arXiv)

Text-to-image diffusion models show great potential in synthesizing a large variety of concepts in new compositions and scenarios. However, the latent space of initial seeds is still not well understood and its structure was shown to impact the generation of various concepts. Specifically, simple operations like interpolation and finding the centroid of a set of seeds perform poorly when using standard Euclidean or spherical metrics in the latent space. This paper makes the observation that, in current training procedures, diffusion models observed inputs with a narrow range of norm values. This has strong implications for methods that rely on seed manipulation for image generation, with applications to few-shot and long-tail learning tasks. To address this issue, we propose a novel method for interpolating between two seeds and demonstrate that it defines a new non-Euclidean metric that takes into account a norm-based prior on seeds. We describe a simple yet efficient algorithm for approximating this interpolation procedure and use it to further define centroids in the latent seed space. We show that our new interpolation and centroid techniques significantly enhance the generation of rare concept images. This further leads to state-of-the-art performance on few-shot and long-tail benchmarks, improving prior approaches in terms of generation speed, image quality, and semantic content.