Diffusion-Based Auctions for Multi-Winner Banner Ads

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

cs.GTOct 10, 2026

Diffusion-Based Auctions for Multi-Winner Banner Ads

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

Organizations: Harvard · MIT

Abstract

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.

Figures & tables

Panel of Figure 1 — Sampled images for $3$ agents with captions “Louis Vuitton bag”, “H&M storefront” and “Nike shoes” and (normalized) bids $b_{1}$ , $b_{2}$ and $b_{3}$ respectively, for different choices of $(b_{1},b_{2},b_{3})$ .

Figure 2: If the expected alignment between the generated image and bidder $i$ ’s caption were increasing in bidder $i$ ’s bid, we would be able to straightforwardly adapt the payment rule from Myerson’s lemma to compute prices that induce truthful reporting of types a dominant strategy.

Base Prompt	Agent 1 Prompt	Agent 2 Prompt
Two friends chatting over coffee at a cafe	Starbucks mug	Apple MacBook Air
A hiker resting on a mountain trail	North Face backpack	Gatorade bottle
A woman with a tray of food at a cafeteria	McDonald’s fries	Pepsi can
A person walking down a city street	Louis Vuitton handbag	H&M storefront
Friends gathered for a movie night at home	Doritos chips	Coca-Cola cans
A car driving along a scenic coastal highway	Tesla car	ExxonMobil sign

Table 1: Example prompt configurations across 2-Agent scenarios

Panel of Figure 3 — Figure 3: Allocation rule outputs for 2 agents, North Face and Gatorade, with bids $(b_{1},b_{2})$ .

Panel of Figure 4 — Figure 4: Alignment of the image output by the allocation rule with a particular bidder’s caption as they vary their bid from $0$ to $1$ in increments of $0.05$ , while keeping the opposing agent’s bid fixed at $0.3$ . For each bid combination and prompt configuration, $k=5$ images are generated per trial across $5$ trials; the welfare-maximizing image is selected within each trial, and CLIP alignment scores are averaged across the $5$ trials and the two prompts. Shaded regions indicate standard deviation.

Panel of Figure 5 — Figure 5: Percent improvement of the welfare from our allocation rule over the single-winner baseline, averaged across all prompts in the two-agent and the five-agent settings respectively. We use $k=20$ Monte Carlo samples in the allocation rule, for each prompt and bid combination.

Figure 6: Welfare improvement is most significant when agents bid similar values.

Figure 7: $k=5$ Monte Carlo samples in the allocation rule attain more than 90% of the welfare improvement over the single-winner baseline attained with $k=20$ .

Panel of Figure 8 — Figure 8: Allocation rule (top) and relative regret from truthful bidding (bottom) under the Myerson payment rule, with Agent 2’s bid fixed at $b_{2}=0.3$ and Agent 1’s bid varied over $[0,1]$ in increments of $0.05$ . The allocation rule uses $k=5$ diffusion samples. To estimate the expected alignment induced by our allocation rule we sample from the allocation rule $5$ times and average the alignment scores from these $5$ repetitions. Relative regret stays below $4\%$ across all true values, confirming near incentive compatibility.

Panel of Figure 9 — Figure 9: Relative regret from truthful bidding under the Clarke payment rule for the exact same settings as those in Figure 8 . The allocation rule uses $k=5$ diffusion samples. To estimate the (ex ante) Clarke payments and utilities, we run the allocation rule $5$ times and average the results. The relative regret is worse than that under Myerson lemma-based payments, by about an order of magnitude.

Panel of Figure 10 — Figure 10: Relative and absolute ex post regret of Agent 1, for $k=25$ and $k=50$ Monte Carlo samples in the allocation rule, for 5 different prompt configurations in the two-agent setting, and averaged over possible values of the agents in a grid over $[0,1]\times[0,1]$ .

Figure 11: LAION image quality scores in the 3-agent setting. Scores are shown for different bid configurations for the agents. Scores are averaged across all the prompt configurations we consider in Appendix A .

Base Prompt	Agent 1 Prompt	Agent 2 Prompt
Someone drinking from a coffee cup in an office meeting	Starbucks coffee cup	Dunkin coffee cup
A person drinking from a beverage can while working at a desk	Coca-Cola can	Pepsi can
Someone wearing athletic shoes while jogging in a park	Nike running shoes	Adidas running shoes

Table 2: Example prompt configurations in 2-Agent competitive scenarios

Panel of Figure 12 — Figure 12: Competitive 2-agent bidding results.

Panel of Figure 13 — Figure 13: Allocation analysis for competitive 2-agent scenario.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Base Prompt	Agent 1 Prompt	Agent 2 Prompt	Agent 3 Prompt
Two friends chatting over coffee at a cafe	Starbucks mug	Apple MacBook Air	New York Times newspaper
People enjoying a sunny day at the beach	Wilson volleyball	Red Bull cooler	Banana Boat sunscreen
A person relaxing on a living-room sofa	Lay’s potato chips	M&M’s candy	Netflix show on TV
A hiker resting on a mountain trail	North Face backpack	Gatorade bottle	Garmin watch
A professional working at a desk in a bright office	Dell monitor	Deer Park water bottle	Moleskine notebook
A woman with a tray of food at a cafeteria	McDonald’s fries	Pepsi can	Heinz ketchup packet

Appendix

Table 3: Example prompt configurations across

20

three-agent scenarios

Number of Agents	Number of Prompts
2	200
3	133
5	85
10	44
20	25

Appendix

Table 4: Number of Prompts per Agent Configuration

Figure 14: Linear aggregation function without the joint score fails to produce compositional images.

Panel of Figure 15 — Figure 15: Welfare improvement over single-winner baseline from 2 to 20 agents with varying bid combinations, exhibiting up to 23% increase in the 5 agent setting.

Panel of Figure 16 — Figure 16: LAION aesthetic quality scores for varying numbers of agents. Scores are shown for different bid configurations for the agents. Scores are computed across all the prompt configurations we consider in Appendix A . Scores consistently remain above 5.75 across, indicating high image quality is preserved regardless of the number of agents or bid configurations.

Table 21

Panel of Figure 17 — Figure 17: Welfare improvement over the single-winner baseline as a function of the number $k$ of Monte Carlo samples in the allocation rule. For 2, 3, 5, 10 agents, welfare improvement plateaus around $k=5$ samples, where it reaches at least 90% of the welfare improvement attained with $k=20$ . For 20 agents, there is room for improvement beyond $k=5$ , but $k=15$ attains at least 95% of the welfare improvement at $k=20$ .

Base Prompt	Agent 1 Prompt	Agent 2 Prompt
A person drinking from a beverage can while working at a desk	Coca-Cola can	Pepsi can
Someone wearing athletic shoes while jogging in a park	Nike running shoes	Adidas running shoes
A person wearing a smartwatch while exercising at the gym	Apple Watch	Samsung Galaxy Watch
Someone drinking from a water bottle during a yoga class	Hydro Flask water bottle	Yeti water bottle
A driver filling up their car at a gas station	Shell gas station	Chevron gas station
A customer holding a shopping bag from a clothing store	Zara shopping bag	H&M shopping bag

Appendix

Table 7: Prompt configurations across

20

two-agent competitive scenarios

Combination Name	Bid Values
Equal Split 0.50	$(0.50,0.50)$
Dominant 0.70	$(0.30,0.70)$
Dominant 0.90	$(0.10,0.90)$

Appendix

Table 8: Bid Combinations for 2 Bidders

Combination Name	Bid Values
Equal Split 0.33	$(0.33,0.33,0.33)$
Two Dominant 0.40	$(0.40,0.40,0.20)$
Two Dominant 0.50	$(0.50,0.50,0.00)$
Dominant 0.50	$(0.50,0.30,0.20)$
Dominant 0.60	$(0.60,0.30,0.10)$
Dominant 0.60	$(0.60,0.20,0.20)$

Appendix

Table 9: Bid Combinations for 3 Bidders

Combination Name	Bid Values
Equal Split 0.20	$(0.20,0.20,0.20,0.20,0.20)$
Three Dominant 0.25	$(0.25,0.25,0.25,0.15,0.10)$
Two Dominant 0.30	$(0.30,0.30,0.20,0.10,0.10)$
Dominant 0.40	$(0.40,0.30,0.20,0.05,0.05)$
Dominant 0.50	$(0.50,0.25,0.15,0.07,0.03)$
Dominant 0.60	$(0.60,0.20,0.10,0.05,0.05)$

Appendix

Table 10: Bid Combinations for 5 Bidders

Combination Name	Bid Values
Equal Split 0.10	$(0.10,0.10,0.10,0.10,0.10,0.10,0.10,0.10,0.10,0.10)$
Three Dominant 0.20	$(0.20,0.20,0.20,0.15,0.10,0.05,0.05,0.03,0.01,0.01)$
Dominant 0.25	$(0.25,0.20,0.15,0.12,0.10,0.08,0.05,0.03,0.01,0.01)$
Dominant 0.30	$(0.30,0.20,0.15,0.12,0.10,0.07,0.04,0.01,0.00,0.01)$
Dominant 0.35	$(0.35,0.15,0.12,0.10,0.08,0.07,0.05,0.04,0.02,0.02)$

Appendix

Table 11: Bid Combinations for 10 Bidders

Combination Name	Bid Values
Equal Split 0.05	$(0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,$
	$0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05,0.05)$
Four Dominant 0.10	$(0.10,0.10,0.10,0.10,0.08,0.08,0.08,0.07,0.07,0.07,$
	$0.05,0.05,0.05,0.02,0.02,0.02,0.01,0.01,0.01,0.01)$
Dominant 0.15	$(0.15,0.12,0.10,0.08,0.07,0.06,0.05,0.05,0.04,0.04,$
	$0.03,0.03,0.02,0.02,0.02,0.01,0.01,0.01,0.01,0.01)$

Appendix

Table 12: Bid Combinations for 20 Bidders

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DiffAuction: An Auction-Driven Framework for Generative Image Advertising

Diffusion models enable multiple advertisers to compete for exposure within a shared generated image. Yet existing approaches are computationally costly when generating images under varying target-share configurations, and it remains unclear how the resulting outcomes should be evaluated and priced. To address these gaps, we propose DiffAuction, a framework integrating controllable generation, click-intent evaluation, and auction design. First, our training-free Residual Share Calibration (RSC) decomposes joint-attention updates into product-specific residuals and rescales them according to target shares. We further introduce Share-Conditioned Prompting (SCP) to adapt the viewpoint to each desired allocation. Second, we develop an evaluator that uses a VLM to extract visual evidence and an LLM to assess Click-Through Intent (CTI), a proxy for click propensity, along four dimensions: Product Prominence, Brand Recognizability, Scene Integration, and Contextual Value Communication. We validate its assessments against judgments from 10 trained annotators on 1000 images. Third, we formulate this advertising setting as an auction over jointly feasible generation configurations. Each configuration has a public expected CTI vector, while advertisers hold configuration-specific private values per unit of CTI that map click intent into commercial value. We adopt a learnable affine maximizer auction (AMA), which jointly selects a shared generation configuration and determines advertiser-specific payments to maximize expected platform revenue. The resulting allocation and payment rules guarantee dominant-strategy incentive compatibility (DSIC) and individual rationality (IR). Experiments show that our generation method strengthens the monotonic relationship between target shares and CTI relative to baselines, while the learned AMA achieves higher platform revenue in the resulting auction setting.

Yijie Su, Ruiyang Si, Tonghan Wang

Tongji University · Tsinghua University · Shanghai Qi Zhi Institute

Image Generation Controllable Image Generation Mechanism Design Image Generation Evaluation Multi-Subject Image Generation

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May 29, 2026

Model Monotonicity in Autobidding Auctions: When Do Better Predictions Lead to Better Outcomes?

Online advertising platforms rely on machine learning models to predict click-through rates (pCTR) and conversion rates (pCVR) for auction mechanisms. We introduce a novel framework to study the interaction between recommender system model quality, auction format, and autobidder behavior. We formalize when model improvements -- defined via a refinement relation inspired by filtrations in probability theory -- lead to improvements in platform-level Evaluation Criteria Metrics (ECM) such as revenue, welfare, or liquid welfare. Our main contributions are: (1) a formal definition of model improvement based on cluster refinement, and (2) a systematic characterization of ECM monotonicity across different combinations of bidder types (tCPA, max-CPA), auction formats (first-price, second-price, VCG), and budget constraints. We show that first-price auctions with uniform bidding guarantee revenue monotonicity for tCPA bidders without budgets (via Jensen's inequality), while second-price auctions and budget constraints can break this property. We provide full numerical constructions for the non-monotonicity results. Our findings have practical implications for advertising platforms seeking to align model improvements with business outcomes.

Ashwinkumar Badanidiyuru

Uber Technologies, Inc., San Francisco, CA, USA.

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Oct 22, 2026

Truthful by Omission: Click Thinning for LLM-Native Advertising

Generative AI assistants are becoming an advertising medium, embedding sponsored content in their answers. This setting departs from classical position auctions in two ways: an ad's click-through rate depends on the passage that hosts it, and because users stop at their first click, earlier ads take clicks from later ones. This competition for clicks makes truthfulness delicate: a higher bid can reshape the allocation and put a competitor ahead of the bidder, reducing the bidder's clicks. Existing mechanisms either attain a constant fraction of the optimal welfare (advertisers' total click value) but are not known to be truthful, or are truthful but their welfare guarantee degrades as the number of passages grows. We achieve both even when the answer and its editorial order are fixed before bidding. Assuming each ad's click-through rate when reached is known and unaffected by omitting other ads, we give a computationally efficient mechanism that is truthful in expectation and attains at least half the optimal welfare under free reordering. Our key idea, click thinning, omits ads at random, showing earlier ads less often so that each ad's overall click probability no longer depends on the order of the ads. Welfare maximization then reduces to a tractable matching problem, and solving it exactly with VCG-style payments makes truthful bidding optimal in expectation. Characterizing the click probabilities that omission can achieve sharpens the approximation factor from

2

2-(1-δ)^{K-1}

when at most

K

ads are shown and each click-through rate is at most

δ

. This factor is the best possible for any order-preserving rule, even one that ignores incentives and computation, so truthfulness and computational efficiency incur no additional worst-case loss.

Junhua Liu, Zhicheng Liang, Zejun Zhang +2

University of Southern California, Los Angeles, USA · The Chinese University of Hong Kong, Shenzhen, Shenzhen, China · University of Illinois Chicago, Chicago, USA

Online Advertising Mechanism Design

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