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Diffusion-Based Auctions for Multi-Winner Banner Ads

Lilian Sun, Henry Huang, Fucheng Warren Zhu, Giannis Daras, Constantinos Daskalakis

arXiv:2610.14473v1cs.GTcs.AIcs.LG

TL;DR

Single-winner banner-ad auctions may leave efficiency unrealized, motivating a richer allocation space that can combine advertisers’ preferences. The paper uses bid-weighted caption scores to guide diffusion-model image generation and selects a high-welfare candidate. Experiments report improved welfare, bid monotonicity, and approximate incentive compatibility without degrading image quality.

  • Problem

    Single-winner banner-ad auctions may leave economic efficiency unrealized, while richer outcomes require natural images that aggregate advertiser preferences according to bid strength.

    Source: §1 · p. 3

  • Method

    The mechanism combines bidders’ bids and captions into a composite diffusion score, samples candidate images, and selects the image with highest welfare.

    Source: §1 · p. 5

  • Results

    Experiments show welfare improvement over single-winner baselines, approximate incentive compatibility, and bid monotonicity without degrading image quality.

    Source: §1 · p. 6, §6 · p. 22

  • Takeaways & Limitations

    Diffusion models can support banner-ad mechanisms that mix advertisers’ content in a selected image while attaining higher welfare than standard single-winner mechanisms.

    Source: §5 · p. 21

    Because the natural-image allocation space lacks an analytical description, Monte Carlo sampling only approximately optimizes welfare, so truthfulness remains approximate and some welfare may be left on the table.

    Source: §5 · p. 21

Abstract

from arXiv · show

We propose a new framework for banner ad auctions, leveraging diffusion models to allow for multiple bidders to co-win a single banner ad opportunity, and in particular influence the ad shown on the banner depending on the strength of their bids, enabling a far richer outcome space compared to standard banner ad auctions, where there is a single winner who shows their ad. In our framework, the outcomes are images (what ad to show) and each bidder expresses their preferences over outcomes by declaring their value per unit of alignment between the image chosen by the mechanism and a textual description of their desired image. Our proposed mechanism combines the advertisers' bids and textual descriptions into a score that drives the reverse process of a diffusion model. This is used to sample a set of candidate images from which the welfare maximizing one is eventually chosen. Extensive experimentation evaluates our proposed mechanism around the following axes: (1) efficiency improvements of our allocation rule relative to the single-winner allocation rule; (2) monotonicity of our allocation rule; and (3) approximate incentive compatibility when combining our allocation rule with Myerson lemma-based or Clarke rule-based payments. Improvements along all these axes are shown with the number of Monte Carlo samples. Meanwhile, these benefits are attained while preserving the image quality.

1 Introduction

The paper studies whether diffusion models can expand banner-ad auctions beyond choosing one advertiser’s ad, while producing natural images that combine advertisers’ preferences according to their bids. It proposes a diffusion-based allocation rule and evaluates welfare, monotonicity, and incentive compatibility.

1 Introduction

  • Single-winner ad auctions may leave efficiency unrealized; the challenge is to produce natural images that aggregate advertiser preferences according to bid strength.The paper investigates combining mechanism design with diffusion models to address this challenge.Source: §1 · p. 3
  • A continuous image outcome space can combine multiple advertisers’ preferences in one banner, unlike selecting among a finite set of bidder-specific banners.The paper situates this as a way for generative models to address discrete allocation limits in mechanism design for digital goods.Source: §1 · p. 3
  • Each bidder’s value is private type times image-caption alignment, while a system caption encodes basic image desiderata and the auction seeks to maximize welfare.The allocation space comprises all images of a fixed resolution.Source: §1 · p. 4
  • The allocation rule aggregates bid-weighted caption scores in a reverse diffusion process, samples k images, and selects the one with highest welfare.Generation time scales with the reverse process and number of samples, creating a time–welfare trade-off.Source: §1 · p. 5
  • Myerson-based pricing uses bidder alignment over bids, while VCG-style pricing compares other bidders’ welfare with and without a bidder using sampled images.Approximate monotonicity and numerical integration limit the former; the latter does not guarantee incentive compatibility, though deviation incentives decline as k increases.Source: §1 · pp. 5–6
  • Experiments show welfare improvement over single-winner baselines, approximate incentive compatibility, and bid monotonicity without degrading image quality.These properties are demonstrated across multi-agent experiments on a diverse dataset.Source: §1 · p. 6

2 Related Work

Related work has explored mechanism design for generated text, while leaving image generation and diffusion-based mechanisms as open directions. The paper builds on diffusion models’ controllability to integrate multiple agents’ preferences.

2.1 Mechanism Design and Generative AI

  • Prior generative-AI auction work addresses generated text, leaving open mechanism design for other modalities and generative models, including images and diffusion.The paper’s focus is improving attainable welfare in existing auction settings by expanding the allocation space.Source: §2.1 · p. 7

2.2 Controllable Image Generation with Diffusion Models

  • Diffusion models reverse a gradual noising process to generate images, and guidance can steer outputs toward desired attributes without a separate classifier.The paper uses this controllability as a basis for an allocation rule that integrates multiple agents’ preferences.Source: §2.2 · p. 7

3 Methodology

The methodology frames image generation as an auction over natural images, then combines bidder preferences through diffusion-based allocation and approximate payment rules. It targets welfare improvement, approximate monotonicity, and approximate incentive compatibility.

3 Methodology

  • The auction seeks welfare improvement over single-winner baselines, approximate monotonicity, and approximate incentive compatibility.Its design pairs an allocation rule that generates a high-welfare image with a payment rule intended to support good incentive properties.Source: §3 · p. 7

3.1.1 Auctions and Social Welfare

  • Social-welfare maximization over natural images is difficult because feasible natural images lack a mathematical specification and bidder preferences are hard to express.If values were known and optimization over natural images were possible, VCG could maximize welfare truthfully; the paper uses diffusion sampling to approximate optimization instead.Source: §3.1.1 · p. 8, §3.3 · p. 9

3.1.2 Score-Based Diffusion and Guidance

  • Diffusion models learn scores for progressively noised images, which can drive reverse diffusion from noise toward clean samples, including samples conditioned on captions.Classifier-Free Guidance sharpens generation by steering the unconditional score toward the conditional score.Source: §3.1.2 · p. 8

3.2 Our Setting: Image Generation Auctions

  • Each bidder has a public caption and private scalar type, with value equal to that type times the image-caption alignment score.The paper uses CLIP for alignment; a base prompt may specify image content and guardrails.Source: §3.2 · p. 9

3.3 A Prelude: the VCG auction

  • The VCG allocation would maximize welfare over natural images, but the paper instead accesses that image space through diffusion models and approximate sampling.The natural-image set is not mathematically specified in a form amenable to exact optimization.Source: §3.3 · p. 9

3.4 Our Allocation Rule: From Bids and Captions to High-Welfare Images via Score Composition

  • A recursively composed score aggregates bids and captions to guide reverse diffusion; the mechanism samples k candidate images and selects the one maximizing submitted-bid welfare.For two bidders, score composition interpolates between a score conditioned on both prompts and one conditioned on the highest bidder’s prompt; the weight depends on relative bids.Source: §3.4 · p. 10

3.5.1 Computing Prices Using Myerson’s Lemma.

  • The Myerson-based payment rule uses expected alignment as the allocation quantity, but approximate monotonicity and numerical integration introduce incentive-compatibility error.Randomized score curves can be sampled for different bids to estimate prices in expectation; increasing grid points can control numerical integration error, though computation is slow.Source: §3.5.1 · p. 11

3.5.2 Computing Prices Using Clarke’s Payment Rule.

  • The Clarke-inspired rule charges an approximation of other bidders’ welfare loss, computed from images sampled with and without bidder i; it is easier to compute but does not guarantee truthful bidding.Experiments report weaker approximate truthfulness than for Myerson-based payments, with deviation incentives decreasing as k increases; the approach is not tied to public captions and private scalar values, though caption manipulation was not tested.Source: §3.5.2 · p. 12

4 Results

Across experiments spanning different prompts and bidder counts, the allocation rule improved welfare over a single-winner baseline and showed approximately monotone alignment and near-truthful bidding under tested payment rules. Image quality remained high, including in competitive-brand scenarios.

4.1 Experimental Setup

  • The evaluation covered more than 80,000 image generations across everyday base prompts paired with bidder prompts from technology, food, fashion, and automobile sectors to analyze allocation and payment rule properties.Images were generated with FLUX.1-schnell using 5 inference steps and guidance scale 10; welfare was computed using CLIP alignment.Source: §4.1 · pp. 12–13

4.2 Bid Monotonicity: Prompt Alignment Increases with Bid

  • Alignment with an agent’s prompt was approximately non-decreasing as its bid rose, with the opposing bid fixed at 0.3.The curves average across repetitions and two prompt configurations; shaded regions show standard deviation.Source: §4.2 · p. 14, Figure 4 · p. 14

4.3 Efficiency: Improved Welfare Compared to Single-Winner Baseline

  • Average welfare improved by up to 15.4% in the 2-agent setting and 23.0% in the 5-agent setting over the single-winner baseline.These maxima occurred when bids were equal: both normalized bids were 0.5 for two agents and all five were 0.2.Source: Figure 5 · p. 15, §4.3 · p. 15
  • For specific prompt and bid combinations, welfare gains reached 21% in the 2-agent setting and 36.0% in the 5-agent setting.For compatible prompts, the largest improvement occurred when agents bid similar values; the authors attribute this to balanced bids activating cooperative potential in their score composition.Source: §4.3 · p. 15, Figure 6 · p. 15
  • With up to 10 agents, k = 5 samples achieved at least 90% of the welfare improvement attained with k = 20; for 20 agents, k = 15 achieved a similar effect.The welfare improvement plateaued beyond k = 5 in the reported settings, suggesting moderate sample counts realize benefits where latency matters.Source: §4.3 · p. 16, Figure 7 · p. 16

4.4 Incentive Compatibility

  • Under Myerson-based payments, relative regret stayed below 4% across tested true values, while Clarke-based payments were mostly below 10% but about an order of magnitude worse.The Myerson result used two representative prompts in a two-agent setting; Clarke ex ante regret used the same settings and k = 5 allocation samples.Source: §4.4.1 · p. 16, Figure 8 · p. 17, §4.4.2 · p. 17

4.5 Image Quality Preservation; 4.6 Competitive Bidding

  • LAION scores exceeded 5.75 across tested agent counts and bid configurations; competitive-brand scenarios retained welfare gains up to 3% and approximate bid monotonicity.For three agents, scores ranged from 5.77 to 6.02; competitive scenarios also had LAION scores above 5.75.Source: Figure 11 · p. 18, §4.5 · p. 19, §4.6 · p. 20

5 Discussion

The discussion frames diffusion-based auctions as a way to expand advertising outcomes and combine advertisers’ content. It also notes that richer image spaces and sampling limit optimization and create a trade-off between economic and computational efficiency.

5 Discussion

  • The mechanism combines advertisers’ content in generated banner images and attains higher welfare than single-winner mechanisms with approximate truthfulness.The discussion presents this as an example of generative AI creating opportunities to improve welfare.Source: §5 · p. 21
  • A platform could use the mechanism to generate banner images reflecting multiple advertisers’ preferences, with visibility and influence aligned to their bids.The discussion also suggests extending the approach to branded product placement in video.Source: §5 · p. 21
  • Because natural images lack an analytical description, the mechanism uses diffusion sampling and can only approximately optimize welfare and truthfulness.More samples improve welfare and reduce sampling variance, but increase computational resources and generation time.Source: §5 · p. 21
  • Future work includes studying prompt manipulation, richer bidding languages, revenue-maximizing mechanisms, and extension to modalities such as video.The paper also identifies bidder directives about content or competitor co-existence as a research direction.Source: §5 · p. 21

6 Conclusion

The conclusion reports improved welfare over single-winner baselines and approximate incentive compatibility for diffusion-based image auctions. The appendices describe prompt configurations and a recursive score composition for multiple agents.

6 Conclusion

  • The empirical analysis reports improved social welfare over single-winner baselines and good incentive properties across diverse prompt and bid combinations, including settings with up to 20 agents.The conclusion describes score composition as controlling sampled content according to prompts and bid strengths, alongside payment rules for approximate incentive compatibility.Source: §6 · p. 22

A Prompts

  • The prompt set pairs generated everyday scenes with real-world brand prompts from product categories including food, technology, fashion, automotive, and energy.The appendix includes example configurations for 20 three-agent scenarios and a table of prompt counts by agent configuration.Source: A Prompts · p. 24, Table 3 · p. 24, Table 4 · p. 25

B Generalized Score Composition

  • For multiple agents, the score composition is defined recursively from compositions for fewer agents, with agents ordered by decreasing bids and prompts concatenated across agents.The appendix also introduces normalized weights and a conditional score for the dominant agent’s prompt.Source: B Generalized Score Composition · p. 25

C Linear Aggregation

Linear aggregation of bidder-specific scores failed to produce compositional images, instead yielding visually incoherent overlays.

C Linear Aggregation

  • The authors report that the linear aggregation function did not yield compositional images.The figure caption specifies that the failed function omitted the joint score.Source: C Linear Aggregation · p. 26, Figure 14 · p. 26
  • Linear aggregation produced faded objects overlaid on one another rather than compositional images.Figure 14 identifies this failure of the linear aggregation function without the joint score.Source: C Linear Aggregation · p. 26, Figure 14 · p. 26

D.1 Welfare Improvement

Figure 15 reports welfare improvement over the single-winner baseline across settings with 2 to 20 agents and varying bid combinations.

D.1 Welfare Improvement

  • Up to 23% welfare improvement over the single-winner baseline is reported in the 5-agent setting.Figure 15 covers settings from 2 to 20 agents with varying bid combinations.Source: Figure 15 · p. 28

D.2 LAION Image Quality

LAION aesthetic quality scores remain above 5.75 across the tested agent counts and bid configurations.

D.2 LAION Image Quality

  • LAION aesthetic quality scores stay above 5.75 across the tested numbers of agents and bid configurations.Scores are computed across the prompt configurations considered in Appendix A.Source: Figure 16 · p. 30

D.3 Image Quality using CLIP Alignment

Tables 5 and 6 report image quality using CLIP alignment scores for two- and three-agent settings.

D.3 Image Quality using CLIP Alignment

  • Tables 5 and 6 report CLIP alignment image-quality scores across prompt configurations and bid combinations for two- and three-agent settings.Table 5 covers two agents; Table 6 covers three agents.Source: Table 5 · p. 31, Table 6 · p. 31

D.4 Monte Carlo Samples Ablation

The Monte Carlo ablation compares welfare improvement across sample counts, alongside competitive-bidding scenarios and bid-combination configurations.

D.4 Monte Carlo Samples Ablation

  • For 2, 3, 5, and 10 agents, k = 5 reaches at least 90% of the welfare improvement at k = 20; for 20 agents, k = 15 reaches at least 95%.For 20 agents, improvement can continue beyond k = 5.Source: Figure 17 · p. 33

D.5 Competitive Bidding

  • Table 7 lists prompt configurations for 20 two-agent competitive scenarios.Source: Table 7 · p. 34

E Bid Combination Values

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