Gaussian-Mixture Latent Flow for Stochastic 3D Human Motion Prediction

Yue Ma; Frederick W. B. Li; Xiaohui Liang

cs.CVAug 21, 2026

Gaussian-Mixture Latent Flow for Stochastic 3D Human Motion Prediction

Authors: Yue Ma, Frederick W. B. Li, Xiaohui Liang

Organizations: Beihang University · Durham University · Zhongguancun Laboratory

Abstract

Stochastic human motion prediction aims to forecast future motion distributions. Although recent studies have achieved strong performance in terms of accuracy and diversity, they often overlook plausibility (e.g., resulting in physically unrealistic predictions) and uncertainty quantification, both of which are essential for real-world applications and downstream tasks. To address these issues, we propose a latent flow-based model equipped with a data-driven Gaussian mixture prior that more effectively disentangles diverse human behaviors than conventional single-modal priors. This prior is derived from patterns in the training data without requiring additional annotations. Furthermore, the fully invertible nature of our model enables natural uncertainty quantification through tractable likelihood computation. Experiments on the Human3.6M and AMASS datasets demonstrate that our approach achieves state-of-the-art performance in both accuracy and plausibility.

Figures & tables

Panel of Figure 1 — Figure 1: Unlike prior approaches, our method (1) introduces a mixed Gaussian prior to effectively disentangle diverse human motion patterns, improving plausibility by reducing semantic entanglement, and (2) incorporates a fully invertible architecture that supports exact likelihood computation, thereby providing a principled means of uncertainty estimation.

Figure 2: Overview of the framework. We predict future motion within a latent space constructed by a flow model. Owing to the invertibility of normalizing flows, a single model can function as both an encoder and a decoder through its forward and inverse processes, respectively. During latent forecasting, we first pad the observed sequence to the full length using the final observed frame and transform it into the latent space to obtain the starting point $\mathbf{Z}_{0}$ . In training, the model learns the velocity field that maps $p_{\mathbf{Z}_{0}}=\mathcal{N}(\mathbf{Z}_{0},\mathrm{I})$ to $\mathbf{Z}_{1}$ , corresponding to the ground-truth future. In inference, we employ an ODE solver to evolve the latent state over time, and the resulting latent codes are decoded to generate the final motion predictions.

			Human3.6M [ 32 ]							AMASS [ 51 ]
Multi Modal	UA	Method	Diversity	Accuracy		Multi-modal Accuracy		Plausibility		Diversity	Accuracy		Multi-modal Accuracy		Plausibility
Multi Modal	UA	Method	APD $\uparrow$	ADE $\downarrow$	FDE $\downarrow$	MMADE $\downarrow$	MMFDE $\downarrow$	CMD $\downarrow$	FID $\downarrow$	APD $\uparrow$	ADE $\downarrow$	FDE $\downarrow$	MMADE $\downarrow$	MMFDE $\downarrow$	CMD $\downarrow$
✗	✗	TPK [ 68 ]	6.723	0.461	0.560	0.522	0.569	6.326	0.538	9.283	0.656	0.675	0.658	0.674	17.127
✗	✗	DLow [ 77 ]	11.741	0.425	0.518	0.495	0.531	4.927	1.255	13.170	0.590	0.612	0.618	0.617	15.185
✗	✗	GSPS [ 53 ]	14.757	0.389	0.496	0.476	0.525	10.758	2.103	12.465	0.563	0.613	0.609	0.633	18.404
✗	✓	Motron [ 61 ]	7.168	0.375	0.488	0.509	0.539	40.796	13.743	-	-	-	-	-	-

Table 1: Quantitative results compared to stochastic baselines adopting Best-of-50 metrics on the Human3.6M and AMASS datasets. As AMASS does not include action labels, FID is not used for evaluation. The best results are highlighted in bold , second best are underlined .

Panel of Figure 3 — Figure 3: Qualitative results. We present qualitative comparison results with SkeletonDiff [ 15 ] , CoMusion [ 63 ] , TransFusion [ 66 ] , and BeLFusion [ 3 ] on the AMASS dataset. For each method, we visualize the final frame of 10 randomly sampled predictions.

	Human3.6M [ 32 ]							AMASS [ 51 ]
	APD $\uparrow$	ADE $\downarrow$	FDE $\downarrow$	MMADE $\downarrow$	MMFDE $\downarrow$	CMD $\downarrow$	FID $\downarrow$	APD $\uparrow$	ADE $\downarrow$	FDE $\downarrow$	MMADE $\downarrow$	MMFDE $\downarrow$	CMD $\downarrow$
Ours	4.804	0.333	0.399	0.471	0.464	3.015	0.088	7.144	0.461	0.474	0.540	0.509	8.579
w/ Fixed Gaussian	4.676	0.336	0.407	0.478	0.475	2.767	0.133	7.311	0.463	0.474	0.541	0.509	9.583
w/ Standard Normal	5.056	0.356	0.421	0.483	0.479	5.854	0.143	7.339	0.465	0.477	0.545	0.511	10.706
w/ FM Only	4.553	0.341	0.408	0.480	0.475	4.895	0.156	7.521	0.469	0.475	0.546	0.509	12.563
w/o Past	5.008	0.346	0.419	0.478	0.478	2.917	0.223	7.531	0.479	0.486	0.557	0.513	8.849

Table 2: The results of ablation studies on the Human3.6M and AMASS datasets. Since AMASS does not include action labels, FID is not used for evaluation. The best results are highlighted in bold .

Panel of Table 3 — Table 3: The results of log-likelihood $\uparrow$ on the Human3.6M and AMASS datasets.

Appendix figures & tables9 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 4 — Figure 4: Visualization of the multi-modal latent space. We present a 2D t-SNE projection of the latent encodings for all Human3.6M test sequences: (a) colored by their nearest sub-distribution, and (b) colored by the action label of each sequence.

Panel of Figure 5 — Figure 5: Visualization of the single-modal latent space. We present a 2D t-SNE projection of the latent encodings for all Human3.6M test sequences, which is colored by the action label.

Prior	Nums	APD $\uparrow$	ADE $\downarrow$	FDE $\downarrow$	MMADE $\downarrow$	MMFDE $\downarrow$	CMD $\downarrow$	FID $\downarrow$
Single	-	5.056	0.356	0.421	0.483	0.479	5.854	0.143
MM	1	4.691	0.338	0.408	0.476	0.475	3.215	0.154
MM	8	4.773	0.334	0.403	0.473	0.469	3.038	0.134
MM	16	4.804	0.333	0.399	0.471	0.464	3.015	0.088
MM	32	4.885	0.333	0.400	0.475	0.470	2.955	0.092

Appendix

Table 4: Analysis of varying the number of initialized sub-distributions used to construct the latent space, with results reported on Human3.6M.

Method	Steps	Time	Human3.6M [ 32 ]
Method	Steps	Time	APD $\uparrow$	ADE $\downarrow$	FDE $\downarrow$	MMADE $\downarrow$	MMFDE $\downarrow$
Dopri5	-	504ms	5.046	0.335	0.401	0.472	0.465
Euler	1	16ms	1.196	0.367	0.513	0.513	0.571
Euler	10	88ms	3.427	0.330	0.409	0.476	0.477
Euler	20	174ms	4.069	0.330	0.400	0.472	0.468
Euler	100	886ms	4.804	0.333	0.399	0.471	0.464

Appendix

Table 5: Experimental results on various ODE solvers.

Panel of Figure 6 — Figure 6: We evaluate the correlation between prediction errors ( ADE and FDE ) and their associated uncertainty ranks (denoted ”Eval”) on Human3.6M and AMASS. As a reference benchmark, we also present the values based on ideal ranks (denoted ”GT”).

Panel of Table 6 — Table 6: The area discrepancy in the error distribution.

Panel of Figure 7 — Figure 7: Qualitative results. We present qualitative comparison results with CoMusion [ 63 ] and SLD [ 72 ] on Human3.6M (top), and with CoMusion [ 63 ] and SkeletonDiff [ 15 ] on AMASS (bottom). In each group, the final row shows visualizations weighted by uncertainty as estimated by our model, with greater opacity indicating higher probability.

	Walking				Eating				Smoking				Discussion
Milliseconds	80	160	320	400	80	160	320	400	80	160	320	400	80	160	320	400
ResGRU [ 54 ]	0.28	0.49	0.72	0.81	0.23	0.39	0.62	0.76	0.23	0.39	0.62	0.76	0.31	0.68	1.01	1.09
DMGNN [ 40 ]	0.18	0.31	0.49	0.58	0.17	0.30	0.49	0.59	0.21	0.39	0.81	0.77	0.26	0.65	0.92	0.99
Hisrep [ 52 ]	0.18	0.30	0.46	0.51	0.16	0.29	0.49	0.60	0.22	0.40	0.86	0.80	0.20	0.52	0.78	0.87
KD-Former [ 16 ]	0.15	0.32	0.54	0.61	0.14	0.28	0.50	0.51	0.17	0.37	0.76	1.46	0.19	0.53	0.87	0.90
MSTP-Net [ 12 ]	0.19	0.34	0.50	0.54	0.16	0.29	0.50	0.61	0.21	0.40	0.80	0.78	0.21	0.54	0.79	0.83

Appendix

Table 7: The results of short-term prediction (

\leq

400ms) compared to baselines on Human3.6M. The best results are highlighted in bold .

	Walking				Eating				Smoking				Discussion
Milliseconds	560	720	880	1000	560	720	880	1000	560	720	880	1000	560	720	880	1000
ResGRU [ 54 ]	0.93	-	-	1.03	0.95	-	-	1.08	1.25	-	-	1.50	1.43	-	-	1.69
DMGNN [ 40 ]	0.66	-	-	0.75	0.74	-	-	1.14	0.83	-	-	1.52	1.33	-	-	1.45
Hisrep [ 52 ]	0.59	0.62	0.61	0.64	0.74	0.81	1.01	1.10	0.86	1.00	1.35	1.58	1.29	1.51	1.66	1.63
KD-Former [ 16 ]	0.70	-	-	0.69	0.71	-	-	1.08	1.01	-	-	1.46	1.24	-	-	1.69
MSTP-Net [ 12 ]	0.60	0.66	0.67	0.68	0.72	0.78	0.96	1.08	0.86	0.98	1.30	1.51	1.22	1.42	1.49	1.51

Appendix

Table 8: The results of long-term prediction (

\geq

560ms) compared to baselines on Human3.6M. The best results are highlighted in bold .

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