# Designing a Conditional Prior Distribution for Flow-Based Generative Models

arXiv: https://arxiv.org/abs/2502.09611 · HTML: https://mlsanity.com/paper/2502.09611/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 13 Feb 2025.

## Builds on (most cited first, 30 of 31)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [CLIPScore: A Reference-free Evaluation Metric for Image Captioning](https://mlsanity.com/paper/2104.08718/) (2021)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Deep Unsupervised Clustering with Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/1611.02648/) (2016)
- [Variational Deep Embedding: An Unsupervised and Generative Approach to Clustering](https://mlsanity.com/paper/1611.05148/) (2016)
- [Flow Matching in Latent Space](https://mlsanity.com/paper/2307.08698/) (2023)
- [PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Prior](https://mlsanity.com/paper/2106.06406/) (2021)
- [Semi-Supervised Learning with Normalizing Flows](https://mlsanity.com/paper/1912.13025/) (2019)
- [Generative Pre-training for Speech with Flow Matching](https://mlsanity.com/paper/2310.16338/) (2023)
- [Meta Flow Matching: Integrating Vector Fields on the Wasserstein Manifold](https://mlsanity.com/paper/2408.14608/) (2024)
- [Latent Space Editing in Transformer-Based Flow Matching](https://mlsanity.com/paper/2312.10825/) (2023)
- [Extended Flow Matching: a Method of Conditional Generation with Generalized Continuity Equation](https://mlsanity.com/paper/2402.18839/) (2024)

## Built on by (most cited first, 10 of 10)

- [Better Source, Better Flow: Learning Condition-Dependent Source Distribution for Flow Matching](https://mlsanity.com/paper/2602.05951/) (2026)
- [Colored Noise Diffusion Sampling](https://mlsanity.com/paper/2605.30332/) (2026)
- [Optimal Transport Flow Matching by Design](https://mlsanity.com/paper/2606.04092/) (2026)
- [CaloTrilogy: Toward a Breakthrough in One-Step, End-to-End, Physics-Guided Shower Generation for Modern Calorimeters](https://mlsanity.com/paper/2606.04165/) (2026)
- [Adapting Noise to Data: Generative Flows from 1D Processes](https://mlsanity.com/paper/2510.12636/) (2025)
- [Flow Matching with Optimized Subclass Priors for Medical Image Augmentation](https://mlsanity.com/paper/2605.16469/) (2026)
- [Source-Lifted Flow Matching for Intervenable Multimodal Imitation](https://mlsanity.com/paper/2607.10206/) (2026)
- [CARE: Condition-Aware Representation Regularization for Diffusion Models](https://mlsanity.com/paper/2609.28561/) (2026)
- [GRFBrain: Graph-Structured Rectified Flows for EEG Dynamic Modeling](https://mlsanity.com/paper/2609.37934/) (2026)
- [Guidance Without Labels: Flow Matching from Coupled Gaussian Mixtures](https://mlsanity.com/paper/2610.16654/) (2026)

## Abstract (arXiv)

Flow-based generative models have recently shown impressive performance for conditional generation tasks, such as text-to-image generation. However, current methods transform a general unimodal noise distribution to a specific mode of the target data distribution. As such, every point in the initial source distribution can be mapped to every point in the target distribution, resulting in long average paths. To this end, in this work, we tap into a non-utilized property of conditional flow-based models: the ability to design a non-trivial prior distribution. Given an input condition, such as a text prompt, we first map it to a point lying in data space, representing an ``average" data point with the minimal average distance to all data points of the same conditional mode (e.g., class). We then utilize the flow matching formulation to map samples from a parametric distribution centered around this point to the conditional target distribution. Experimentally, our method significantly improves training times and generation efficiency (FID, KID and CLIP alignment scores) compared to baselines, producing high quality samples using fewer sampling steps.