  Heatmap-based methods dominate in the field of human pose estimation by
modelling the output distribution through likelihood heatmaps. In contrast,
regression-based methods are more efficient but suffer from inferior
performance. In this work, we explore maximum likelihood estimation (MLE) to
develop an efficient and effective regression-based methods. From the
perspective of MLE, adopting different regression losses is making different
assumptions about the output density function. A density function closer to the
true distribution leads to a better regression performance. In light of this,
we propose a novel regression paradigm with Residual Log-likelihood Estimation
(RLE) to capture the underlying output distribution. Concretely, RLE learns the
change of the distribution instead of the unreferenced underlying distribution
to facilitate the training process. With the proposed reparameterization
design, our method is compatible with off-the-shelf flow models. The proposed
method is effective, efficient and flexible. We show its potential in various
human pose estimation tasks with comprehensive experiments. Compared to the
conventional regression paradigm, regression with RLE bring 12.4 mAP
improvement on MSCOCO without any test-time overhead. Moreover, for the first
time, especially on multi-person pose estimation, our regression method is
superior to the heatmap-based methods. Our code is available at
https://github.com/Jeff-sjtu/res-loglikelihood-regression
