# PROUD: PaRetO-gUided Diffusion Model for Multi-objective Generation

arXiv: https://arxiv.org/abs/2407.04493 · HTML: https://mlsanity.com/paper/2407.04493/

## 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 30 of its 67 references that are in the map.
- First posted on arXiv 5 Jul 2024.

## Placed in

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

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Multi-Task Learning as Multi-Objective Optimization](https://mlsanity.com/paper/1810.04650/) (2018)
- [Plug and Play Language Models: A Simple Approach to Controlled Text Generation](https://mlsanity.com/paper/1912.02164/) (2019)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [How to Train Your Energy-Based Models](https://mlsanity.com/paper/2101.03288/) (2021)
- [Disentangled and Controllable Face Image Generation via 3D Imitative-Contrastive Learning](https://mlsanity.com/paper/2004.11660/) (2020)
- [Protein Design with Guided Discrete Diffusion](https://mlsanity.com/paper/2305.20009/) (2023)
- [StyleDiffusion: Controllable Disentangled Style Transfer via Diffusion Models](https://mlsanity.com/paper/2308.07863/) (2023)
- [Towards Unsupervised Learning of Generative Models for 3D Controllable Image Synthesis](https://mlsanity.com/paper/1912.05237/) (2019)
- [Accelerating Bayesian Optimization for Biological Sequence Design with Denoising Autoencoders](https://mlsanity.com/paper/2203.12742/) (2022)
- [Multi-Objective GFlowNets](https://mlsanity.com/paper/2210.12765/) (2022)
- [Towards Understanding and Improving GFlowNet Training](https://mlsanity.com/paper/2305.07170/) (2023)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [Learning Latent Subspaces in Variational Autoencoders](https://mlsanity.com/paper/1812.06190/) (2018)
- [EditVAE: Unsupervised Part-Aware Controllable 3D Point Cloud Shape Generation](https://mlsanity.com/paper/2110.06679/) (2021)
- [Controllable Data Generation by Deep Learning: A Review](https://mlsanity.com/paper/2207.09542/) (2022)
- [Pareto Navigation Gradient Descent: a First-Order Algorithm for Optimization in Pareto Set](https://mlsanity.com/paper/2110.08713/) (2021)
- [Outpainting by Queries](https://mlsanity.com/paper/2207.05312/) (2022)
- [Multi-objective Deep Data Generation with Correlated Property Control](https://mlsanity.com/paper/2210.01796/) (2022)
- [A Pareto-optimal compositional energy-based model for sampling and optimization of protein sequences](https://mlsanity.com/paper/2210.10838/) (2022)
- [Robust Generative Adversarial Network](https://mlsanity.com/paper/2004.13344/) (2020)
- [An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation](https://mlsanity.com/paper/2208.01362/) (2022)

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

- [Gradient-Based Multi-Objective Deep Learning: Algorithms, Theories, Applications, and Beyond](https://mlsanity.com/paper/2501.10945/) (2025)
- [ParetoFlow: Guided Flows in Multi-Objective Optimization](https://mlsanity.com/paper/2412.03718/) (2024)
- [Offline Model-Based Optimization: Comprehensive Review](https://mlsanity.com/paper/2503.17286/) (2025)
- [Multi-Objective-Guided Discrete Flow Matching for Controllable Biological Sequence Design](https://mlsanity.com/paper/2505.07086/) (2025)
- [TR2-D2: Tree Search Guided Trajectory-Aware Fine-Tuning for Discrete Diffusion](https://mlsanity.com/paper/2509.25171/) (2025)
- [Pareto Low-Rank Adapters: Efficient Multi-Task Learning with Preferences](https://mlsanity.com/paper/2407.08056/) (2024)
- [Multi-objective Deep Learning: Taxonomy and Survey of the State of the Art](https://mlsanity.com/paper/2412.01566/) (2024)
- [Calibrating Generative Models to Distributional Constraints](https://mlsanity.com/paper/2510.10020/) (2025)
- [AReUReDi: Annealed Rectified Updates for Refining Discrete Flows with Multi-Objective Guidance](https://mlsanity.com/paper/2510.00352/) (2025)
- [Stroke of Surprise: Progressive Semantic Illusions in Vector Sketching](https://mlsanity.com/paper/2602.12280/) (2026)
- [ParetoSlider: Diffusion Models Post-Training for Continuous Reward Control](https://mlsanity.com/paper/2604.20816/) (2026)
- [Learning Design-Score Manifold to Guide Diffusion Models for Offline Optimization](https://mlsanity.com/paper/2506.05680/) (2025)
- [Amortized Active Generation of Pareto Sets](https://mlsanity.com/paper/2510.21052/) (2025)
- [Sample-Efficient Optimisation over the Outputs of Generative Models](https://mlsanity.com/paper/2509.23800/) (2025)
- [Reflection Separation from a Single Image via Joint Latent Diffusion](https://mlsanity.com/paper/2606.04107/) (2026)
- [Traversing the Satisfaction-Diversity Frontier in Text-to-Image Diffusion](https://mlsanity.com/paper/2610.02372/) (2026)

## Abstract (arXiv)

Recent advancements in the realm of deep generative models focus on generating samples that satisfy multiple desired properties. However, prevalent approaches optimize these property functions independently, thus omitting the trade-offs among them. In addition, the property optimization is often improperly integrated into the generative models, resulting in an unnecessary compromise on generation quality (i.e., the quality of generated samples). To address these issues, we formulate a constrained optimization problem. It seeks to optimize generation quality while ensuring that generated samples reside at the Pareto front of multiple property objectives. Such a formulation enables the generation of samples that cannot be further improved simultaneously on the conflicting property functions and preserves good quality of generated samples. Building upon this formulation, we introduce the PaRetO-gUided Diffusion model (PROUD), wherein the gradients in the denoising process are dynamically adjusted to enhance generation quality while the generated samples adhere to Pareto optimality. Experimental evaluations on image generation and protein generation tasks demonstrate that our PROUD consistently maintains superior generation quality while approaching Pareto optimality across multiple property functions compared to various baselines.