# Boomerang: Local sampling on image manifolds using diffusion models

arXiv: https://arxiv.org/abs/2210.12100 · HTML: https://mlsanity.com/paper/2210.12100/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 49 of its 66 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Placed in

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

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [LAION-400M: Open Dataset of CLIP-Filtered 400 Million Image-Text Pairs](https://mlsanity.com/paper/2111.02114/) (2021)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [HiFi-GAN: Generative Adversarial Networks for Efficient and High Fidelity Speech Synthesis](https://mlsanity.com/paper/2010.05646/) (2020)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Blended Diffusion for Text-driven Editing of Natural Images](https://mlsanity.com/paper/2111.14818/) (2021)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [In-Domain GAN Inversion for Real Image Editing](https://mlsanity.com/paper/2004.00049/) (2020)
- [A Survey of Data Augmentation Approaches for NLP](https://mlsanity.com/paper/2105.03075/) (2021)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction](https://mlsanity.com/paper/2112.05146/) (2021)

## Built on by (most cited first, 16 of 16)

- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Generalization through variance: how noise shapes inductive biases in diffusion models](https://mlsanity.com/paper/2504.12532/) (2025)
- [Image retrieval outperforms diffusion models on data augmentation](https://mlsanity.com/paper/2304.10253/) (2023)
- [AI-Generated Images as Data Source: The Dawn of Synthetic Era](https://mlsanity.com/paper/2310.01830/) (2023)
- [Synthetic Data as Validation](https://mlsanity.com/paper/2310.16052/) (2023)
- [Forte : Finding Outliers with Representation Typicality Estimation](https://mlsanity.com/paper/2410.01322/) (2024)
- [U-Turn Diffusion](https://mlsanity.com/paper/2308.07421/) (2023)
- [GeNIe: Generative Hard Negative Images Through Diffusion](https://mlsanity.com/paper/2312.02548/) (2023)
- [One-to-Normal: Anomaly Personalization for Few-shot Anomaly Detection](https://mlsanity.com/paper/2502.01201/) (2025)
- [DiffBatt: A Diffusion Model for Battery Degradation Prediction and Synthesis](https://mlsanity.com/paper/2410.23893/) (2024)
- [Internal Representations of Vision Models Through the Lens of Frames on Data Manifolds](https://mlsanity.com/paper/2211.10558/) (2022)
- [Hummingbird: High Fidelity Image Generation via Multimodal Context Alignment](https://mlsanity.com/paper/2502.05153/) (2025)
- [Do We Need All the Synthetic Data? Targeted Image Augmentation via Diffusion Models](https://mlsanity.com/paper/2505.21574/) (2025)
- [Music Boomerang: Reusing Diffusion Models for Data Augmentation and Audio Manipulation](https://mlsanity.com/paper/2507.04864/) (2025)
- [GeoEdit: Local Frames for Fast, Training-Free On-Manifold Editing in Diffusion Models](https://mlsanity.com/paper/2604.24238/) (2026)
- [JIVE: Jacobian-Informed Volume Expansion for Diverse Generative Sampling](https://mlsanity.com/paper/2609.33906/) (2026)

## Abstract (arXiv)

The inference stage of diffusion models can be seen as running a reverse-time diffusion stochastic differential equation, where samples from a Gaussian latent distribution are transformed into samples from a target distribution that usually reside on a low-dimensional manifold, e.g., an image manifold. The intermediate values between the initial latent space and the image manifold can be interpreted as noisy images, with the amount of noise determined by the forward diffusion process noise schedule. We utilize this interpretation to present Boomerang, an approach for local sampling of image manifolds. As implied by its name, Boomerang local sampling involves adding noise to an input image, moving it closer to the latent space, and then mapping it back to the image manifold through a partial reverse diffusion process. Thus, Boomerang generates images on the manifold that are ``similar,'' but nonidentical, to the original input image. We can control the proximity of the generated images to the original by adjusting the amount of noise added. Furthermore, due to the stochastic nature of the reverse diffusion process in Boomerang, the generated images display a certain degree of stochasticity, allowing us to obtain local samples from the manifold without encountering any duplicates. Boomerang offers the flexibility to work seamlessly with any pretrained diffusion model, such as Stable Diffusion, without necessitating any adjustments to the reverse diffusion process. We present three applications for Boomerang. First, we provide a framework for constructing privacy-preserving datasets having controllable degrees of anonymity. Second, we show that using Boomerang for data augmentation increases generalization performance and outperforms state-of-the-art synthetic data augmentation. Lastly, we introduce a perceptual image enhancement framework, which enables resolution enhancement.