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Continuous Normalizing Flows for Uncertainty-Aware Human Pose Estimation

Shipeng Liu, Ziliang Xiong, Bastian Wandt, Per-Erik Forssén

TL;DR

This work tackles uncertainty-aware Human Pose Estimation (HPE) by marrying regression with Continuous Normalizing Flows (CNFs) to model complex, non-fixed data distributions without increasing inference cost. The proposed Continuous Flow Residual Estimation (CFRE) uses a reparameterized residual framework and a decoupled training regime (Regression + CNF flow) with Flow Matching-based optimization to improve both localization accuracy and calibrated uncertainty. Key innovations include a tractable upper-bound training objective, efficient trace estimation via the Hutchinson estimator, and evaluation on COCO and Human3.6M showing improved mAP and uncertainty metrics (AUSE, AURG) while maintaining competitive GFLOPs. The method demonstrates that CNFs provide flexible, anisotropic, and heavier-tailed distribution modeling that aligns better with real-world pose data, enabling robust, uncertainty-aware 2D/3D HPE suitable for practical deployment.

Abstract

Human Pose Estimation (HPE) is increasingly important for applications like virtual reality and motion analysis, yet current methods struggle with balancing accuracy, computational efficiency, and reliable uncertainty quantification (UQ). Traditional regression-based methods assume fixed distributions, which might lead to poor UQ. Heatmap-based methods effectively model the output distribution using likelihood heatmaps, however, they demand significant resources. To address this, we propose Continuous Flow Residual Estimation (CFRE), an integration of Continuous Normalizing Flows (CNFs) into regression-based models, which allows for dynamic distribution adaptation. Through extensive experiments, we show that CFRE leads to better accuracy and uncertainty quantification with retained computational efficiency on both 2D and 3D human pose estimation tasks.

Continuous Normalizing Flows for Uncertainty-Aware Human Pose Estimation

TL;DR

This work tackles uncertainty-aware Human Pose Estimation (HPE) by marrying regression with Continuous Normalizing Flows (CNFs) to model complex, non-fixed data distributions without increasing inference cost. The proposed Continuous Flow Residual Estimation (CFRE) uses a reparameterized residual framework and a decoupled training regime (Regression + CNF flow) with Flow Matching-based optimization to improve both localization accuracy and calibrated uncertainty. Key innovations include a tractable upper-bound training objective, efficient trace estimation via the Hutchinson estimator, and evaluation on COCO and Human3.6M showing improved mAP and uncertainty metrics (AUSE, AURG) while maintaining competitive GFLOPs. The method demonstrates that CNFs provide flexible, anisotropic, and heavier-tailed distribution modeling that aligns better with real-world pose data, enabling robust, uncertainty-aware 2D/3D HPE suitable for practical deployment.

Abstract

Human Pose Estimation (HPE) is increasingly important for applications like virtual reality and motion analysis, yet current methods struggle with balancing accuracy, computational efficiency, and reliable uncertainty quantification (UQ). Traditional regression-based methods assume fixed distributions, which might lead to poor UQ. Heatmap-based methods effectively model the output distribution using likelihood heatmaps, however, they demand significant resources. To address this, we propose Continuous Flow Residual Estimation (CFRE), an integration of Continuous Normalizing Flows (CNFs) into regression-based models, which allows for dynamic distribution adaptation. Through extensive experiments, we show that CFRE leads to better accuracy and uncertainty quantification with retained computational efficiency on both 2D and 3D human pose estimation tasks.
Paper Structure (24 sections, 33 equations, 5 figures, 5 tables)

This paper contains 24 sections, 33 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Heatmap-based Methods
  4. Regression-based Methods
  5. Method
  6. Regression Paradigm
  7. Reparameterization
  8. Negative Log-Likelihood Estimation with CNFs
  9. Density Transformation via CNFs
  10. Optimizing the NLL
  11. Trace Estimation with the Hutchinson Trace Estimator (HTE).
  12. Training of the Model
  13. Decoupled Training Strategy
  14. Continuous Normalizing Flows Training
  15. Heteroscedastic Regression Network Training
  16. ...and 9 more sections

Figures (5)

  • Figure 1: Overview of our proposed method. Heteroscedastic Deep Regression (Blue box) estimates the mean and scale of keypoint locations, which can be described as a simple distribution (e.g., Gaussian or Laplacian). Our CNF then transforms this into a more complex uncertainty distribution.
  • Figure 2: The proposed CFRE architecture. The yellow box is our contribution.
  • Figure 3: Contour plot of joint estimations across multiple human instances. First column: Input images (Red: Samples; Green: Mean value); Second column: Estimation with Gaussian assumption; Third column: Estimation with Laplace assumption; Fourth column: Distributions learned by CNFs. Fifth column: Distributions learned by NFs. Rows correspond to different human instances and their joint estimations: (1) left elbow, (2) right knee.
  • Figure 4: Impact of Hyperparameter $c$ on AP metrics.
  • Figure 5: Sparsification Error Plots Comparing Different Regression Methods.