# PG-MAP: Joint MAP Optimization for Inference-Time Alignment of Diffusion and Flow-Matching Models

arXiv: https://arxiv.org/abs/2606.22958 · HTML: https://mlsanity.com/paper/2606.22958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 30 of its 31 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [An Image is Worth One Word: Personalizing Text-to-Image Generation using Textual Inversion](https://mlsanity.com/paper/2208.01618/) (2022)
- [Scaling Autoregressive Models for Content-Rich Text-to-Image Generation](https://mlsanity.com/paper/2206.10789/) (2022)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (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)
- [Diffusion Model Alignment Using Direct Preference Optimization](https://mlsanity.com/paper/2311.12908/) (2023)
- [Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2301.13826/) (2023)
- [Universal Guidance for Diffusion Models](https://mlsanity.com/paper/2302.07121/) (2023)
- [Hard Prompts Made Easy: Gradient-Based Discrete Optimization for Prompt Tuning and Discovery](https://mlsanity.com/paper/2302.03668/) (2023)
- [D-Flow: Differentiating through Flows for Controlled Generation](https://mlsanity.com/paper/2402.14017/) (2024)
- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [Inference-Time Alignment of Diffusion Models with Direct Noise Optimization](https://mlsanity.com/paper/2405.18881/) (2024)
- [On the Guidance of Flow Matching](https://mlsanity.com/paper/2502.02150/) (2025)
- [Steering Rectified Flow Models in the Vector Field for Controlled Image Generation](https://mlsanity.com/paper/2412.00100/) (2024)
- [GLASS Flows: Transition Sampling for Alignment of Flow and Diffusion Models](https://mlsanity.com/paper/2509.25170/) (2025)
- [Diffusion Adaptive Text Embedding for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2510.23974/) (2025)
- [Safeguarding Text-to-Image Generation via Inference-Time Prompt-Noise Optimization](https://mlsanity.com/paper/2412.03876/) (2024)
- [Diffusion Blend: Inference-Time Multi-Preference Alignment for Diffusion Models](https://mlsanity.com/paper/2505.18547/) (2025)
- [Training-Free Reward-Guided Image Editing via Trajectory Optimal Control](https://mlsanity.com/paper/2509.25845/) (2025)
- [Alignment of Diffusion Model and Flow Matching for Text-to-Image Generation](https://mlsanity.com/paper/2602.00413/) (2026)

## Abstract (arXiv)

Inference-time alignment of pretrained text-to-image models is typically performed along a single control axis, such as classifier-free guidance, attention editing, or reward-based latent perturbations. This limitation prevents modeling joint dependencies between conditioning and latent variables and hinders transfer across generative transports. We propose PG-MAP, a training-free framework that formulates inference-time alignment as a trajectory-level Gibbs-MAP / proximal energy optimization over the conditioning c and latent state zt via a forward-consistency coupling, optionally guided by a frozen preference reward. This joint formulation enables coordinated updates across modalities while remaining compatible with both diffusion and flow-matching models through transport-specific adaptations. Across diffusion backbones (SD~1.5, SDXL), PG-MAP consistently improves alignment metrics such as PickScore and Aesthetic, and can be effectively combined with tuned classifier-free guidance to achieve the strongest overall performance. On flow-matching models (SD3.5-medium), the framework reduces to a latent-only variant, achieving 91.9% PickScore and 75.7% HPS win rates against a static baseline, with controlled experiments ruling out noise-related artifacts. Human evaluations further confirm consistent preference over strong baselines, including tuned CFG and compute-matched universal guidance. Finally, an oracle-routing analysis shows that the relative importance of conditioning and latent optimization depends on prompt types, surfacing further headroom that a per-prompt selector could exploit.