# Structured Output Learning with Conditional Generative Flows

arXiv: https://arxiv.org/abs/1905.13288 · HTML: https://mlsanity.com/paper/1905.13288/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 30 of 37)

- [Parallel Rectangle Flip Attack: A Query-based Black-box Attack against Object Detection](https://mlsanity.com/paper/2201.08970/) (2022)
- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [Generalizable Black-Box Adversarial Attack with Meta Learning](https://mlsanity.com/paper/2301.00364/) (2023)
- [Towards Robust Physical-world Backdoor Attacks on Lane Detection](https://mlsanity.com/paper/2405.05553/) (2024)
- [Controllable Data Generation by Deep Learning: A Review](https://mlsanity.com/paper/2207.09542/) (2022)
- [Attacks in Adversarial Machine Learning: A Systematic Survey from the Life-cycle Perspective](https://mlsanity.com/paper/2302.09457/) (2023)
- [Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference](https://mlsanity.com/paper/2310.16975/) (2023)
- [AutoStudio: Crafting Consistent Subjects in Multi-turn Interactive Image Generation](https://mlsanity.com/paper/2406.01388/) (2024)
- [TheaterGen: Character Management with LLM for Consistent Multi-turn Image Generation](https://mlsanity.com/paper/2404.18919/) (2024)
- [Neural Conditional Probability for Uncertainty Quantification](https://mlsanity.com/paper/2407.01171/) (2024)
- [Generative Flows with Invertible Attentions](https://mlsanity.com/paper/2106.03959/) (2021)
- [Conditional Injective Flows for Bayesian Imaging](https://mlsanity.com/paper/2204.07664/) (2022)
- [A Review of Change of Variable Formulas for Generative Modeling](https://mlsanity.com/paper/2308.02652/) (2023)
- [Gradual Domain Adaptation via Normalizing Flows](https://mlsanity.com/paper/2206.11492/) (2022)
- [VQ-Flows: Vector Quantized Local Normalizing Flows](https://mlsanity.com/paper/2203.11556/) (2022)
- [Normalizing Flow-based Differentiable Particle Filters](https://mlsanity.com/paper/2403.01499/) (2024)
- [On the Robustness of Normalizing Flows for Inverse Problems in Imaging](https://mlsanity.com/paper/2212.04319/) (2022)
- [Conditional Measurement Density Estimation in Sequential Monte Carlo via Normalizing Flow](https://mlsanity.com/paper/2203.08617/) (2022)
- [Posterior Sampling for Image Restoration using Explicit Patch Priors](https://mlsanity.com/paper/2104.09895/) (2021)
- [CAFLOW: Conditional Autoregressive Flows](https://mlsanity.com/paper/2106.02531/) (2021)
- [Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics](https://mlsanity.com/paper/2104.04391/) (2021)
- [Multiscale Residual Learning of Graph Convolutional Sequence Chunks for Human Motion Prediction](https://mlsanity.com/paper/2308.16801/) (2023)
- [ContextFlow++: Generalist-Specialist Flow-based Generative Models with Mixed-Variable Context Encoding](https://mlsanity.com/paper/2406.00578/) (2024)
- [MANGO: Multimodal Attention-based Normalizing Flow Approach to Fusion Learning](https://mlsanity.com/paper/2508.10133/) (2025)
- [HybridFlow: Quantification of Aleatoric and Epistemic Uncertainty with a Single Hybrid Model](https://mlsanity.com/paper/2510.05054/) (2025)
- [DifAttack++: Query-Efficient Black-Box Adversarial Attack via Hierarchical Disentangled Feature Space in Cross-Domain](https://mlsanity.com/paper/2406.03017/) (2024)
- [Maximum Likelihood on the Joint (Data, Condition) Distribution for Solving Ill-Posed Problems with Conditional Flow Models](https://mlsanity.com/paper/2208.11782/) (2022)
- [Implicit Training of Energy Model for Structure Prediction](https://mlsanity.com/paper/2211.11649/) (2022)
- [Weakly Supervised Label Learning Flows](https://mlsanity.com/paper/2302.09649/) (2023)
- [DTA: Distribution Transform-based Attack for Query-Limited Scenario](https://mlsanity.com/paper/2312.07245/) (2023)

## Abstract (arXiv)

Traditional structured prediction models try to learn the conditional likelihood, i.e., p(y|x), to capture the relationship between the structured output y and the input features x. For many models, computing the likelihood is intractable. These models are therefore hard to train, requiring the use of surrogate objectives or variational inference to approximate likelihood. In this paper, we propose conditional Glow (c-Glow), a conditional generative flow for structured output learning. C-Glow benefits from the ability of flow-based models to compute p(y|x) exactly and efficiently. Learning with c-Glow does not require a surrogate objective or performing inference during training. Once trained, we can directly and efficiently generate conditional samples. We develop a sample-based prediction method, which can use this advantage to do efficient and effective inference. In our experiments, we test c-Glow on five different tasks. C-Glow outperforms the state-of-the-art baselines in some tasks and predicts comparable outputs in the other tasks. The results show that c-Glow is versatile and is applicable to many different structured prediction problems.