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Diffusion Models are Evolutionary Algorithms
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Shows that diffusion models can be interpreted as evolutionary algorithms and proposes Diffusion Evolution (and Latent Space Diffusion Evolution) that optimizes fitness via iterative Bayesian denoising without neural networks.
Problem
Connecting diffusion models and evolutionary algorithms mathematically, and using this link to build evolutionary optimizers that find diverse high-fitness solutions in parameter spaces, including high-dimensional ones.
Approach
Maps fitness to probability density and inverts the diffusion process with Bayes' rule so that the denoised estimate x0 is a fitness-weighted, Gaussian-localized average of the population; this gives a neural-network-free evolutionary algorithm with implicit mutation, selection, recombination and reproductive isolation. Latent Space Diffusion Evolution denoises in a randomly projected low-dimensio
Key results
- On 2D benchmarks Diffusion Evolution attains high elite entropy (e.g., 5.86 on Rosenbrock, 5.23 on Himmelblau) while keeping average fitness near 0.96, whereas CMA-ES and PEPG collapse to entropy near 0.
- Latent Diffusion Evolution solves Cart Pole in 10 generations with population 512 and one evaluation per individual.
- On Rastrigin-256 the latent variant reaches QD-score 70.2 versus 0.14 for MAP-Elites and 0.11 for the non-latent Diffusion Evolution.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use latent-space distances instead of parameter-space distances (ablation) | Diffusion Evolution · Rastrigin 32D | average fitness: 0.02 -> 0.19 | Helped |
| use latent-space distances instead of parameter-space distances (ablation) | Diffusion Evolution · Rastrigin 256D | average fitness: 0.00 -> 0.15 | Helped |
| use cosine alpha scheduling rather than the default DDPM schedule (ablation) | Diffusion Evolution · fitness functions with fewer than 100 evolution steps | performance | Helped |
| use latent-space distances instead of parameter-space distances (ablation) | Diffusion Evolution · Acrobot (scaling 1.0) | average reward: -199.9 -> -127.0 | Helped |
Surprising findings
- Plain Diffusion Evolution performs poorly in high-dimensional Rastrigin settings, with QD-score 0.11 at dimension 256, and latent projection is needed to recover performance.
Limitations
- Plain Diffusion Evolution degrades in high-dimensional parameter spaces.
- Choice of fitness-to-density mapping g and temperature T is task-dependent and hand-tuned.
- Latent variant uses a random projection of dimension d=2 chosen for visualization, not validated as optimal.
Experimental setup
Datasets: synthetic 2D fitness functions (Rosenbrock, Beale, Himmelblau, Ackley, Rastrigin) OpenAI Gym control tasks (Cart Pole, Acrobot, Mountain Car, Pendulum)
Benchmarks: Rosenbrock Beale Himmelblau Ackley Rastrigin (2, 4, 32, 256 dims) Cart Pole Acrobot Mountain Car Pendulum
Metrics: Shannon entropy of elite population average fitness QD-score final reward success rate
Baselines: CMA-ES OpenES PEPG MAP-Elites
Builds on: DDPM DDIM latent diffusion models CMA-ES MAP-Elites
Closest papers by meaning
- A First-order Generative Bilevel Optimization Framework for Diffusion Models (ICML 2025 · similarity 0.88)
- Derivative-Free Guidance in Continuous and Discrete Diffusion Models with Soft Value-based Decoding (NeurIPS 2025 · similarity 0.87)
- Simple Guidance Mechanisms for Discrete Diffusion Models (ICLR 2025 · similarity 0.87)
- Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physics (ICLR 2025 · similarity 0.87)
- TFG: Unified Training-Free Guidance for Diffusion Models (NeurIPS 2024 · similarity 0.87)
- Align Your Steps: Optimizing Sampling Schedules in Diffusion Models (ICML 2024 · similarity 0.86)
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