# Latent Normalizing Flows for Many-to-Many Cross-Domain Mappings

arXiv: https://arxiv.org/abs/2002.06661 · HTML: https://mlsanity.com/paper/2002.06661/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2020.

## Built on by (most cited first, 16 of 16)

- [Make-A-Story: Visual Memory Conditioned Consistent Story Generation](https://mlsanity.com/paper/2211.13319/) (2022)
- [FS-COCO: Towards Understanding of Freehand Sketches of Common Objects in Context](https://mlsanity.com/paper/2203.02113/) (2022)
- [Prompting Hard or Hardly Prompting: Prompt Inversion for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2312.12416/) (2023)
- [SceneTrilogy: On Human Scene-Sketch and its Complementarity with Photo and Text](https://mlsanity.com/paper/2204.11964/) (2022)
- [IC3: Image Captioning by Committee Consensus](https://mlsanity.com/paper/2302.01328/) (2023)
- [Learning Multimodal Data Augmentation in Feature Space](https://mlsanity.com/paper/2212.14453/) (2022)
- [Unity by Diversity: Improved Representation Learning in Multimodal VAEs](https://mlsanity.com/paper/2403.05300/) (2024)
- [Learning Distinct and Representative Styles for Image Captioning](https://mlsanity.com/paper/2209.08231/) (2022)
- [Gradual Domain Adaptation via Normalizing Flows](https://mlsanity.com/paper/2206.11492/) (2022)
- [Text-to-Image Cross-Modal Generation: A Systematic Review](https://mlsanity.com/paper/2401.11631/) (2024)
- [Set Prediction Guided by Semantic Concepts for Diverse Video Captioning](https://mlsanity.com/paper/2312.15720/) (2023)
- [Diverse Image Captioning with Grounded Style](https://mlsanity.com/paper/2205.01813/) (2022)
- [Fiber Bundle Morphisms as a Framework for Modeling Many-to-Many Maps](https://mlsanity.com/paper/2203.08189/) (2022)
- [Constrained Density Matching and Modeling for Cross-lingual Alignment of Contextualized Representations](https://mlsanity.com/paper/2201.13429/) (2022)
- [Variational Transfer Learning using Cross-Domain Latent Modulation](https://mlsanity.com/paper/2205.15523/) (2022)
- [Mapping of Lesion Images to Somatic Mutations](https://mlsanity.com/paper/2512.02162/) (2025)

## Abstract (arXiv)

Learned joint representations of images and text form the backbone of several important cross-domain tasks such as image captioning. Prior work mostly maps both domains into a common latent representation in a purely supervised fashion. This is rather restrictive, however, as the two domains follow distinct generative processes. Therefore, we propose a novel semi-supervised framework, which models shared information between domains and domain-specific information separately. The information shared between the domains is aligned with an invertible neural network. Our model integrates normalizing flow-based priors for the domain-specific information, which allows us to learn diverse many-to-many mappings between the two domains. We demonstrate the effectiveness of our model on diverse tasks, including image captioning and text-to-image synthesis.