# D2D: Detector-to-Differentiable Critic for Improved Numeracy in Text-to-Image Generation

arXiv: https://arxiv.org/abs/2510.19278 · HTML: https://mlsanity.com/paper/2510.19278/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Image generation, text-to-image and editing, one of 14 directions in Diffusion models.
- Builds on 36 of its 39 references that are in the map.
- First posted on arXiv 22 Oct 2025.

## Placed in

- Diffusion models / [Image generation, text-to-image and editing](https://mlsanity.com/diffusion/image-generation-text-to-image-and-editing/)

## Builds on (most cited first, 30 of 36)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Grounding DINO: Marrying DINO with Grounded Pre-Training for Open-Set Object Detection](https://mlsanity.com/paper/2303.05499/) (2023)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Pick-a-Pic: An Open Dataset of User Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2305.01569/) (2023)
- [Human Preference Score v2: A Solid Benchmark for Evaluating Human Preferences of Text-to-Image Synthesis](https://mlsanity.com/paper/2306.09341/) (2023)
- [PixArt-α: Fast Training of Diffusion Transformer for Photorealistic Text-to-Image Synthesis](https://mlsanity.com/paper/2310.00426/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Adversarial Diffusion Distillation](https://mlsanity.com/paper/2311.17042/) (2023)
- [Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2301.13826/) (2023)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [Directly Fine-Tuning Diffusion Models on Differentiable Rewards](https://mlsanity.com/paper/2309.17400/) (2023)
- [YOLOv9: Learning What You Want to Learn Using Programmable Gradient Information](https://mlsanity.com/paper/2402.13616/) (2024)
- [Scaling Open-Vocabulary Object Detection](https://mlsanity.com/paper/2306.09683/) (2023)
- [PixArt-Sigma: Weak-to-Strong Training of Diffusion Transformer for 4K Text-to-Image Generation](https://mlsanity.com/paper/2403.04692/) (2024)
- [Using Human Feedback to Fine-tune Diffusion Models without Any Reward Model](https://mlsanity.com/paper/2311.13231/) (2023)
- [LLM-grounded Diffusion: Enhancing Prompt Understanding of Text-to-Image Diffusion Models with Large Language Models](https://mlsanity.com/paper/2305.13655/) (2023)
- [TallyQA: Answering Complex Counting Questions](https://mlsanity.com/paper/1810.12440/) (2018)
- [Learning To Count Everything](https://mlsanity.com/paper/2104.08391/) (2021)
- [CFG++: Manifold-constrained Classifier Free Guidance for Diffusion Models](https://mlsanity.com/paper/2406.08070/) (2024)
- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [End-to-End Diffusion Latent Optimization Improves Classifier Guidance](https://mlsanity.com/paper/2303.13703/) (2023)
- [CLIP-Count: Towards Text-Guided Zero-Shot Object Counting](https://mlsanity.com/paper/2305.07304/) (2023)
- [CounTR: Transformer-based Generalised Visual Counting](https://mlsanity.com/paper/2208.13721/) (2022)
- [CountGD: Multi-Modal Open-World Counting](https://mlsanity.com/paper/2407.04619/) (2024)

## Built on by (most cited first, 1 of 1)

- [When Do Diffusion Models learn to Generate Multiple Objects?](https://mlsanity.com/paper/2605.00273/) (2026)

## Abstract (arXiv)

Text-to-image (T2I) diffusion models have achieved strong performance in semantic alignment, yet they still struggle with generating the correct number of objects specified in prompts. Existing approaches typically incorporate auxiliary counting networks as external critics to enhance numeracy. However, since these critics must provide gradient guidance during generation, they are restricted to regression-based models that are inherently differentiable, thus excluding detector-based models with superior counting ability, whose count-via-enumeration nature is non-differentiable. To overcome this limitation, we propose Detector-to-Differentiable (D2D), a novel framework that transforms non-differentiable detection models into differentiable critics, thereby leveraging their superior counting ability to guide numeracy generation. Specifically, we design custom activation functions to convert detector logits into soft binary indicators, which are then used to optimize the noise prior at inference time with pre-trained T2I models. Our extensive experiments on SDXL-Turbo, SD-Turbo, and Pixart-DMD across four benchmarks of varying complexity (low-density, high-density, and multi-object scenarios) demonstrate consistent and substantial improvements in object counting accuracy (e.g., boosting up to 13.7% on D2D-Small, a 400-prompt, low-density benchmark), with minimal degradation in overall image quality and computational overhead.