# Flow-based Spatio-Temporal Structured Prediction of Motion Dynamics

arXiv: https://arxiv.org/abs/2104.04391 · HTML: https://mlsanity.com/paper/2104.04391/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 49 of its 83 references that are in the map.
- First posted on arXiv 9 Apr 2021.

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [On human motion prediction using recurrent neural networks](https://mlsanity.com/paper/1705.02445/) (2017)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Learning Trajectory Dependencies for Human Motion Prediction](https://mlsanity.com/paper/1908.05436/) (2019)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [DLow: Diversifying Latent Flows for Diverse Human Motion Prediction](https://mlsanity.com/paper/2003.08386/) (2020)
- [HP-GAN: Probabilistic 3D human motion prediction via GAN](https://mlsanity.com/paper/1711.09561/) (2017)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Human Trajectory Forecasting in Crowds: A Deep Learning Perspective](https://mlsanity.com/paper/2007.03639/) (2020)
- [Noise Flow: Noise Modeling with Conditional Normalizing Flows](https://mlsanity.com/paper/1908.08453/) (2019)
- [Structured Prediction Helps 3D Human Motion Modelling](https://mlsanity.com/paper/1910.09070/) (2019)
- [MT-VAE: Learning Motion Transformations to Generate Multimodal Human Dynamics](https://mlsanity.com/paper/1808.04545/) (2018)

## Built on by (most cited first, 3 of 3)

- [Diffusion Models with Deterministic Normalizing Flow Priors](https://mlsanity.com/paper/2309.01274/) (2023)
- [Multi-Condition Latent Diffusion Network for Scene-Aware Neural Human Motion Prediction](https://mlsanity.com/paper/2405.18700/) (2024)
- [Multiscale Residual Learning of Graph Convolutional Sequence Chunks for Human Motion Prediction](https://mlsanity.com/paper/2308.16801/) (2023)

## Abstract (arXiv)

Conditional Normalizing Flows (CNFs) are flexible generative models capable of representing complicated distributions with high dimensionality and large interdimensional correlations, making them appealing for structured output learning. Their effectiveness in modelling multivariates spatio-temporal structured data has yet to be completely investigated. We propose MotionFlow as a novel normalizing flows approach that autoregressively conditions the output distributions on the spatio-temporal input features. It combines deterministic and stochastic representations with CNFs to create a probabilistic neural generative approach that can model the variability seen in high dimensional structured spatio-temporal data. We specifically propose to use conditional priors to factorize the latent space for the time dependent modeling. We also exploit the use of masked convolutions as autoregressive conditionals in CNFs. As a result, our method is able to define arbitrarily expressive output probability distributions under temporal dynamics in multivariate prediction tasks. We apply our method to different tasks, including trajectory prediction, motion prediction, time series forecasting, and binary segmentation, and demonstrate that our model is able to leverage normalizing flows to learn complicated time dependent conditional distributions.