# BundleFlow: Deep Menus for Combinatorial Auctions by Diffusion-Based Optimization

arXiv: https://arxiv.org/abs/2502.15283 · HTML: https://mlsanity.com/paper/2502.15283/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2025.

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

- [LLM Bidders Preserve the Mechanism-Level Orderings of Human Bidders](https://mlsanity.com/paper/2507.09083/) (2025)
- [Incentive-Aligned Multi-Source LLM Summaries](https://mlsanity.com/paper/2509.25184/) (2025)
- [LLM Active Alignment: A Nash Equilibrium Perspective](https://mlsanity.com/paper/2602.06836/) (2026)
- [One Model, Two Markets: Bid-Aware Generative Recommendation](https://mlsanity.com/paper/2603.22231/) (2026)
- [Duality for Optimal Multi-Item, Multi-Bidder Auction Design: Revenue Certificates through Deep Learning](https://mlsanity.com/paper/2606.10112/) (2026)
- [DiffNash: Finding Nash Equilibrium in High-Dimensional Continuous Action Spaces with Diffusion Policies](https://mlsanity.com/paper/2610.15932/) (2026)

## Abstract (arXiv)

Differentiable economics -- the use of deep learning for auction design -- has driven progress in the automated design of multi-item auctions with additive or unit-demand valuations. However, little progress has been made for optimal combinatorial auctions (CAs), even for the single bidder case, because we need to overcome the challenge of the bundle space growing exponentially with the number of items. For example, when learning a menu of allocation-price choices for a bidder in a CA, each menu element needs to efficiently and flexibly specify a probability distribution on bundles. In this paper, we solve this problem in the single-bidder CA setting by generating a bundle distribution through an ordinary differential equation (ODE) applied to a tractable initial distribution, drawing inspiration from generative models, especially score-based diffusion models and continuous normalizing flow. Our method, BundleFlow, uses deep learning to find suitable ODE-based transforms of initial distributions, one transform for each menu element, so that the overall menu achieves high expected revenue. Our method achieves 1.11-2.23× higher revenue compared with automated mechanism design baselines on the single-bidder version of CATS, a standard CA testbed, and scales to problems with up to 150 items. Relative to a baseline that also learns allocations in menu elements, our method reduces the training iterations by 3.6-9.5× and cuts training time by about 80% in settings with 50 and 100 items.