# EmoDM: A Diffusion Model for Evolutionary Multi-objective Optimization

arXiv: https://arxiv.org/abs/2401.15931 · HTML: https://mlsanity.com/paper/2401.15931/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 29 Jan 2024.

## Placed in

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

## Builds on (most cited first, 11 of 11)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Large Language Models as Evolutionary Optimizers](https://mlsanity.com/paper/2310.19046/) (2023)
- [Pareto Set Learning for Neural Multi-objective Combinatorial Optimization](https://mlsanity.com/paper/2203.15386/) (2022)
- [Large Language Model for Multi-objective Evolutionary Optimization](https://mlsanity.com/paper/2310.12541/) (2023)
- [Multi-Objective Population Based Training](https://mlsanity.com/paper/2306.01436/) (2023)
- [Enhancing Generalization and Scalability for Multi-Objective Optimization with Population Pre-Training](https://mlsanity.com/paper/2312.06125/) (2023)

## Built on by (most cited first, 6 of 6)

- [Diffusion Models are Evolutionary Algorithms](https://mlsanity.com/paper/2410.02543/) (2024)
- [Expensive Multi-Objective Bayesian Optimization Based on Diffusion Models](https://mlsanity.com/paper/2405.08674/) (2024)
- [Heuristically Adaptive Diffusion-Model Evolutionary Strategy](https://mlsanity.com/paper/2411.13420/) (2024)
- [LacaDM: A Latent Causal Diffusion Model for Multiobjective Reinforcement Learning](https://mlsanity.com/paper/2512.19516/) (2025)
- [Remapping and navigation of an embedding space via error minimization: a fundamental organizational principle of cognition in natural and artificial systems](https://mlsanity.com/paper/2601.14096/) (2026)
- [Evolutionary Computation as Natural Generative AI](https://mlsanity.com/paper/2510.08590/) (2025)

## Abstract (arXiv)

Evolutionary algorithms have been successful in solving multi-objective optimization problems (MOPs). However, as a class of population-based search methodology, evolutionary algorithms require a large number of evaluations of the objective functions, preventing them from being applied to a wide range of expensive MOPs. To tackle the above challenge, this work proposes for the first time a diffusion model that can learn to perform evolutionary multi-objective search, called EmoDM. This is achieved by treating the reversed convergence process of evolutionary search as the forward diffusion and learn the noise distributions from previously solved evolutionary optimization tasks. The pre-trained EmoDM can then generate a set of non-dominated solutions for a new MOP by means of its reverse diffusion without further evolutionary search, thereby significantly reducing the required function evaluations. To enhance the scalability of EmoDM, a mutual entropy-based attention mechanism is introduced to capture the decision variables that are most important for the objectives. Experimental results demonstrate the competitiveness of EmoDM in terms of both the search performance and computational efficiency compared with state-of-the-art evolutionary algorithms in solving MOPs having up to 5000 decision variables. The pre-trained EmoDM is shown to generalize well to unseen problems, revealing its strong potential as a general and efficient MOP solver.