DiFF: Doppler-informed Flow Matching for Human Motion Flow

Kai Wang; Mingle Zhao

cs.ROSep 30, 2026

DiFF: Doppler-informed Flow Matching for Human Motion Flow

Authors: Kai Wang, Mingle Zhao

Abstract

Perceiving human motion via privacy-preserving 4D millimeter-wave (mmWave) radar is critical for next-generation human-robot interaction (HRI), where point cloud scene flow serves as a foundational motion representation. Yet the extreme sparsity and noise of 4D radar point clouds make non-rigid motion flow estimation severely ill-posed--a challenge that existing rigid-centric methods and prior works fail to adequately address, largely because they neglect the rich Doppler velocity cues inherent in 4D radar. We propose DiFF, a generative framework that marries Doppler-informed motion priors with a Kolmogorov-Arnold Network (KAN)-based conditional flow matching model. At its core, a KAN-attention mechanism enables expressive feature extraction, while a prior-guided generative process harnesses Doppler cues to regularize the ill-posed solution space. Extensive experiments show that DiFF achieves state-of-the-art (SOTA) performance across diverse real-world datasets, reducing 3D endpoint error to the millimeter scale on the mmBody benchmark.

Figures & tables

Fig. 1: Data pipeline overview. (Left) Dataset setup and multi-modal annotations from [ 4 ] . (Right) Motion label generation from mesh vertices, skeleton, and images, and the proposed Doppler-informed radar motion flow.

Fig. 2: Overview of DiFF. A weight-shared point-wise projection, three KAN blocks, and frame-wise global attention encode the source $\mathrm{PC}_{1}$ and target $\mathrm{PC}_{2}$ . During training, the intermediate flow $\mathcal{S}_{t}$ warps the source points toward the target to construct the state-dependent condition $c_{t}$ . The KAN decoder combines $c_{t}$ , $\mathcal{S}_{t}$ , and the time embedding to predict $v_{\mathrm{pred}}$ . During inference, the condition computed at $t=0$ is cached while the ODE updates $\mathcal{S}_{t}$ .

Fig. 3: The effect of inference steps on EPE3D and average inference time

Model	EPE3D (mm) $\downarrow$	Acc3D Strict (%) $\uparrow$	Acc3D Relax (%) $\uparrow$	0–1 mm (%)	1–10 mm (%)	10–100 mm (%)	100–1000 mm (%)	$>$ 1000 mm (%)	Time (ms) $\downarrow$
FlowNet3D [ 14 ]	1198.131	0.00	0.00	0.00	0.00	0.00	35.56	64.44	11.43
DiffSF [ 46 ]	787.278	1.22	1.38	0.01	0.01	0.46	74.33	25.19	32.87
FLOT [ 47 ]	200.508	1.54	8.53	0.00	0.00	22.53	77.38	0.09	11.07
milliFlow [ 5 ]	177.132	0.00	0.01	0.00	0.00	0.00	99.99	0.01	30.72
DifFlow3D [ 20 ]	120.295	74.39	86.51	0.01	31.24	60.92	4.71	3.12	84.63
FlowStep3D [ 48 ]	84.264	29.63	55.24	0.00	2.66	75.01	22.32	0.01	17.83

TABLE I: Quantitative comparison on the milliFlow dataset. The cumulative error distribution is shown in Fig. 4 (Left). Since milliFlow does not provide Doppler measurements, the DiFF row follows the radial-prior construction described in the experimental setup. Bold marks the best aggregate value, including ties.

Model	EPE3D (mm) $\downarrow$	Acc3D Strict (%) $\uparrow$	Acc3D Relax (%) $\uparrow$	0–1 mm (%)	1–10 mm (%)	10–100 mm (%)	100–1000 mm (%)	$>$ 1000 mm (%)	Time (ms) $\downarrow$
DiffSF [ 46 ]	319.4	4.42	4.60	0.06	0.39	7.32	92.19	0.04	29.90
milliFlow [ 5 ]	80.2	0.03	0.20	0.00	0.00	76.81	23.19	0.00	33.30
FLOT [ 47 ]	30.4	47.44	86.26	0.00	4.03	95.47	0.50	0.00	19.05
FlowNet3D [ 14 ]	14.2	86.01	90.34	0.96	41.83	57.21	0.00	0.00	35.50
FlowStep3D [ 48 ]	13.7	88.96	95.49	0.00	63.50	36.09	0.42	0.00	22.83
DifFlow3D [ 20 ]	2.8	98.63	99.62	2.67	92.24	5.09	0.00	0.00	89.82

TABLE II: Quantitative comparison on the mmBody dataset. The cumulative error distribution is shown in Fig. 4 (Right). Lower EPE3D and inference time are better; higher Acc3D values are better. Bold marks the best aggregate value, including ties.

Fig. 4: Cumulative distributions of per-sample EPE3D on (Left) milliFlow [ 5 ] and (Right) mmBody [ 4 ] , corresponding to Tables I and II , respectively.

Configuration	EPE3D (mm) $\downarrow$
DiFF (Full Model)	2.1
w/o Doppler Prior	4.4
Using MLP	2.7
Static Conditioning	3.3

TABLE III: Ablation study on core components. Configuration names match the variants defined in Section IV .

Variance ( $\sigma^{2}$ )	EPE3D (mm) $\downarrow$	Avg. Training Loss
$1.0$	3.0	$3.20\times 10^{-4}$
$0.1^{2}$	2.3	$9.60\times 10^{-5}$
$\mathbf{0.01^{2}}$	2.1	$3.20\times 10^{-5}$
$0.001^{2}$	2.4	$9.60\times 10^{-6}$
$0.0001^{2}$	2.6	$4.80\times 10^{-6}$
$0.00001^{2}$	3.0	$4.80\times 10^{-6}$

TABLE IV: Sensitivity to noise variance. The lowest EPE3D is highlighted; training loss is reported for reference and is not minimized at the best-EPE3D setting.

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Point Clouds Normalizing Flows Diffusion Models Real-Time Systems

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Sparse and noisy millimeter-wave radar point cloud observations often correspond to multiple plausible human poses, making deterministic pose estimation fundamentally ill-posed. Yet existing radar methods remain deterministic, collapsing this ambiguity into a single estimate. Diffusion-based alternatives can model multi-hypothesis distributions but require costly sequential denoising for each distribution sample and lack calibrated uncertainty. We propose Multi-Hypothesis Normalizing Flow Pose Generator (MH-NFPG), which models pose distributions from radar point clouds using a conditional normalizing flow. Specifically, we combine a spatiotemporal transformer backbone with a normalizing flow that transforms a Laplace base distribution into an expressive posterior, generated in parallel through a single forward pass. Leveraging this efficiency, we outperform diffusion-based alternatives in calibration across three radar benchmarks (MM-Fi, mmRadPose, mRI), improve pose accuracy on two, and match it on the third, while achieving over 20x faster inference for applications and reducing calibration error by up to 85%. We find that calibration degrades substantially for diffusion models, whereas our flow-based approach maintains reliable coverage, also in cross-environment settings. These results demonstrate normalizing flows as a practical alternative to diffusion models for real-time, uncertainty-aware radar pose estimation. Our code will be made publicly available.

Abstract

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