# Residual-Space Evolutionary Optimization via Flow-based Generative Models

arXiv: https://arxiv.org/abs/2606.20084 · HTML: https://mlsanity.com/paper/2606.20084/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Builds on (most cited first, 27 of 27)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [T2I-Adapter: Learning Adapters to Dig out More Controllable Ability for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.08453/) (2023)
- [Null-text Inversion for Editing Real Images using Guided Diffusion Models](https://mlsanity.com/paper/2211.09794/) (2022)
- [StyleCLIP: Text-Driven Manipulation of StyleGAN Imagery](https://mlsanity.com/paper/2103.17249/) (2021)
- [Network Dissection: Quantifying Interpretability of Deep Visual Representations](https://mlsanity.com/paper/1704.05796/) (2017)
- [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)
- [Contrastive Learning for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2007.15651/) (2020)
- [GANSpace: Discovering Interpretable GAN Controls](https://mlsanity.com/paper/2004.02546/) (2020)
- [Zero-shot Image-to-Image Translation](https://mlsanity.com/paper/2302.03027/) (2023)
- [Pivotal Tuning for Latent-based Editing of Real Images](https://mlsanity.com/paper/2106.05744/) (2021)
- [Understanding Deep Image Representations by Inverting Them](https://mlsanity.com/paper/1412.0035/) (2014)
- [Drag Your GAN: Interactive Point-based Manipulation on the Generative Image Manifold](https://mlsanity.com/paper/2305.10973/) (2023)
- [Return of Unconditional Generation: A Self-supervised Representation Generation Method](https://mlsanity.com/paper/2312.03701/) (2023)
- [Explanation by Progressive Exaggeration](https://mlsanity.com/paper/1911.00483/) (2019)
- [Morpho-MNIST: Quantitative Assessment and Diagnostics for Representation Learning](https://mlsanity.com/paper/1809.10780/) (2018)
- [Counterfactual Fairness with Disentangled Causal Effect Variational Autoencoder](https://mlsanity.com/paper/2011.11878/) (2020)
- [CounteRGAN: Generating Realistic Counterfactuals with Residual Generative Adversarial Nets](https://mlsanity.com/paper/2009.05199/) (2020)
- [Diffeomorphic Counterfactuals with Generative Models](https://mlsanity.com/paper/2206.05075/) (2022)
- [LeapFactual: Reliable Visual Counterfactual Explanation Using Conditional Flow Matching](https://mlsanity.com/paper/2510.14623/) (2025)
- [Galaxy Morphology Classification with Counterfactual Explanation](https://mlsanity.com/paper/2510.14655/) (2025)

## Abstract (arXiv)

Data editing with generative methods typically requires differentiable objectives and gradient-based search. However, these assumptions break down in flow-based settings, where edits are performed through forward and backward integration and often involve non-differentiable or black-box objectives. We introduce residual-space evolutionary optimization, a model-agnostic framework that addresses this gap by combining flow-based generative editing with evolutionary algorithms. Building on the observation that conditional flow matching (CFM) can disentangle condition-controlled factors from instance-specific residuals, our framework directly operates in residual space and separates two complementary search regimes: self-pollination performs local exploitation through feature-preserving residual refinement, and cross-pollination promotes broader exploration by recombining residuals across heterogeneous samples. As a proof of concept, we validate on MorphoMNIST, a benchmark dataset for counterfactual generation, and on crystal data, demonstrating that this exploration--exploitation decomposition provides a useful mechanism for balancing target alignment, instance preservation, and diversity, and extends beyond images to real-world scientific domains.