# Calibrating Generative Models to Distributional Constraints

arXiv: https://arxiv.org/abs/2510.10020 · HTML: https://mlsanity.com/paper/2510.10020/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 96 references that are in the map.
- First posted on arXiv 11 Oct 2025.

## Builds on (most cited first, 30 of 41)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Bias and Fairness in Large Language Models: A Survey](https://mlsanity.com/paper/2309.00770/) (2023)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem](https://mlsanity.com/paper/2206.04119/) (2022)
- [Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control](https://mlsanity.com/paper/2409.08861/) (2024)
- [SE(3) diffusion model with application to protein backbone generation](https://mlsanity.com/paper/2302.02277/) (2023)
- [Evaluating model calibration in classification](https://mlsanity.com/paper/1902.06977/) (2019)
- [Fair Diffusion: Instructing Text-to-Image Generation Models on Fairness](https://mlsanity.com/paper/2302.10893/) (2023)
- [Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control](https://mlsanity.com/paper/2402.15194/) (2024)
- [Aligning Language Models with Preferences through f-divergence Minimization](https://mlsanity.com/paper/2302.08215/) (2023)
- [A Distributional Approach to Controlled Text Generation](https://mlsanity.com/paper/2012.11635/) (2020)
- [Finetuning Text-to-Image Diffusion Models for Fairness](https://mlsanity.com/paper/2311.07604/) (2023)
- [Normalizing Flows are Capable Generative Models](https://mlsanity.com/paper/2412.06329/) (2024)
- [Scalable End-to-End Autonomous Vehicle Testing via Rare-event Simulation](https://mlsanity.com/paper/1811.00145/) (2018)

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

- [Bridging the Simulation-to-Experiment Gap with Generative Models using Adversarial Distribution Alignment](https://mlsanity.com/paper/2604.01169/) (2026)
- [The Reward Was in Your Data All Along: Correcting Flow Matching with Discriminator-Guided RL](https://mlsanity.com/paper/2606.19162/) (2026)
- [Calibrating Generative Models to Feature Distributions with MMD Finetuning](https://mlsanity.com/paper/2606.19496/) (2026)
- [A Mean-Field Framework for Inference-Time Distributional Control of Diffusion Models](https://mlsanity.com/paper/2608.08770/) (2026)
- [Scalable Diffusion SBI for Compositional Inference under Simulator Misspecification](https://mlsanity.com/paper/2609.36950/) (2026)
- [SupraTITO: Transferable Generative Molecular Dynamics for Supramolecular Systems](https://mlsanity.com/paper/2610.01381/) (2026)

## Abstract (arXiv)

Generative models frequently suffer miscalibration, wherein statistics of the sampling distribution, such as the fraction of generations in a given class, deviate from desired values. We frame calibration as a constrained optimization problem and seek the closest model in Kullback-Leibler divergence satisfying a calibration constraint. To address the intractability of imposing these constraints exactly, we introduce two surrogate objectives for fine-tuning: (1) the relax loss, which replaces the constraint with a miscalibration penalty, and (2) the reward loss, which converts calibration into a reward fine-tuning problem. We demonstrate that these approaches substantially reduce calibration error across hundreds of simultaneous constraints and models with up to nine billion parameters, spanning applications in protein design, image generation, and language modeling.