# Low-Bit, High-Fidelity: Optimal Transport Quantization for Flow Matching

arXiv: https://arxiv.org/abs/2511.11418 · HTML: https://mlsanity.com/paper/2511.11418/

## 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 13 of its 40 references that are in the map.
- First posted on arXiv 14 Nov 2025.

## 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, 13 of 13)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Flow Matching Guide and Code](https://mlsanity.com/paper/2412.06264/) (2024)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [PTQD: Accurate Post-Training Quantization for Diffusion Models](https://mlsanity.com/paper/2305.10657/) (2023)
- [Q-DiT: Accurate Post-Training Quantization for Diffusion Transformers](https://mlsanity.com/paper/2406.17343/) (2024)
- [PTQ4DiT: Post-training Quantization for Diffusion Transformers](https://mlsanity.com/paper/2405.16005/) (2024)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Beyond FVD: Enhanced Evaluation Metrics for Video Generation Quality](https://mlsanity.com/paper/2410.05203/) (2024)
- [QGAN: Quantized Generative Adversarial Networks](https://mlsanity.com/paper/1901.08263/) (2019)
- [Neural Network Quantization for Microcontrollers: A Comprehensive Survey of Methods, Platforms, and Applications](https://mlsanity.com/paper/2508.15008/) (2025)
- [Diffusion Model Quantization: A Review](https://mlsanity.com/paper/2505.05215/) (2025)
- [The Monge-Kantorovich problem on Wasserstein space](https://mlsanity.com/paper/2406.08585/) (2024)

## Abstract (arXiv)

Flow Matching (FM) generative models offer efficient simulation-free training and deterministic sampling, but their practical deployment is challenged by high-precision parameter requirements. We adapt optimal transport (OT)-based post-training quantization to FM models, minimizing the 2-Wasserstein distance between quantized and original weights, and systematically compare its effectiveness against uniform, piecewise, and logarithmic quantization schemes. Our theoretical analysis provides upper bounds on generative degradation under quantization, and empirical results across five benchmark datasets of varying complexity show that OT-based quantization preserves both visual generation quality and latent space stability down to 2-3 bits per parameter, where alternative methods fail. This establishes OT-based quantization as a principled, effective approach to compress FM generative models for edge and embedded AI applications.