Depth-Distribution Distillation

• Depth-distribution distillation is a neural methodology that transfers structured, probabilistic depth information from a teacher model to a student model.
• It reformulates depth regression into a soft classification task by discretizing depth values and using temperature-scaled softmax and KL-divergence for training.
• Empirical results show that this approach improves accuracy, efficiency, and stability, making it well-suited for real-time multimodal fusion in challenging environments.

Depth-distribution distillation is a neural training methodology wherein depth estimation or depth-related tasks are cast as the transfer of probabilistic or structured depth information (“soft” distributions, priors, or context-encoded knowledge) from an expert teacher model to a lightweight or otherwise constrained student model. Rather than regressing continuous depth values directly, this paradigm encourages the student model to approximate higher-order structural or statistical properties of the teacher’s outputs, promoting robust generalization and improved accuracy even under adverse conditions or data limitations.

1. Reformulation of Depth Regression as Soft Classification

A central mechanic of contemporary depth-distribution distillation, exemplified in XD-RCDepth (Sun et al., 15 Oct 2025), reformulates pixel-wise depth regression as a soft classification task. Rather than predicting a continuous scalar for each pixel, the depth range $[d_{min}, d_{max}]$ is partitioned into $B$ discrete bins with centers $\{c_1, \ldots, c_B\}$. For each pixel $p$, the model calculates the absolute deviation between the predicted depth and each bin center,

$$\Delta_i^{(\cdot)}(p) = |d^{(\cdot)}(p) - c_i|, \quad i=1,\ldots,B$$

where $(\cdot)$ denotes teacher or student. These deviations are negated to logits,

$z_i^{(\cdot)}(p) = -\Delta_i^{(\cdot)}(p)$

which are turned into soft probability distributions via a temperature-scaled softmax,

$$p^{s}(p) = \operatorname{softmax}\left( z^{s}(p)/\tau \right), \quad q^{T}(p) = \operatorname{softmax}\left( z^{T}(p)/\tau \right)$$

This induces a distribution over plausible depth values per pixel, encoding uncertainty and flexibility.

2. KL-Divergence-Based Distillation

Depth-distribution distillation uses the teacher’s soft distribution as the target for the student, minimizing the forward KL divergence: $$L_{D^2\text{-KD}} = \frac{\tau^2}{|\Omega|} \sum_{p \in \Omega} \sum_{i=1}^{B} q_i^T(p) \log\frac{q_i^T(p)}{p_i^{s}(p)}$$ This objective encourages the student model to match not just a single target depth but the teacher’s calibrated uncertainty regarding each depth bin, providing richer supervision especially in ambiguous regions. Typical choices for $\tau$ induce "softness" in the distribution, smoothing optimization and improving gradient flow.

3. Experimental Findings and Model Efficiency

Empirical results presented in (Sun et al., 15 Oct 2025) demonstrate that D²-KD consistently reduces mean absolute error (MAE) in depth estimation tasks, especially for radar-camera fusion networks. In ablation studies, pairing D²-KD with explainability-aligned distillation further decreases MAE (e.g., 2.232 to 2.054 on nuScenes), while maintaining or improving other metrics (RMSE, AbsRel, $\delta_1$ accuracy). The discretized formulation is especially effective for lightweight models, which may struggle to capture minute signal variations in direct regression. By modeling depth uncertainty through bin-wise probabilities, the approach also aligns with model compressibility, leading to parameter, FLOP, and runtime reductions (XD-RCDepth achieves 15 fps and 29.7% fewer parameters versus prior baselines).

4. Optimization and Training Dynamics

Classifying depth into bins using soft targets simplifies optimization compared to direct regression. Soft probability distributions allow for uncertainty modeling, tolerance to ambiguous or noisy teacher predictions, and more stable training. The temperature parameter $\tau$, typically set greater than 1, flattens the probability distribution so that knowledge is transferred about multiple plausible depth values rather than only the most likely one. The KL divergence scales with $\tau^2$ to match gradient magnitudes during distillation.

5. Architectural and Practical Consequences

Depth-distribution distillation is often deployed alongside architectural innovations for multimodal fusion, as in XD-RCDepth’s point-wise DASPP blocks and FiLM-based radar-camera integration. By adopting soft classification, architectures can be designed with lighter computational footprints, real-time processing capabilities, and improved interpretability. This paradigm is particularly well-suited for settings where depth estimation must be robust under sensor noise, illumination variance, or aggressive model compression demands (e.g., for embedded autonomous driving systems).

6. Comparisons and Related Paradigms

Recasting regression as classification with soft targets is recognized as a facilitator for knowledge distillation in dense prediction tasks. Unlike the traditional hard-label regression, depth-distribution distillation captures the teacher’s uncertainty and avoids penalizing the student too harshly for plausible errors. Related works employ similar strategies in semantic segmentation, pose estimation, and more broadly in dense regression, though the discretized probabilistic approach is particularly suited to depth due to inherent ambiguity in range measurements.

Model	Distillation Paradigm	MAE Reduction	FPS
XD-RCDepth	D²-KD (soft bins, KL)	7.97%	~15
Lightweight BL	direct regression	—	~13

7. Implications and Outlook

Depth-distribution distillation supports stable, scalable, and interpretable depth estimation in settings with strict computational boundaries. By leveraging the teacher’s soft output distributions, it is possible to train student models that combine accuracy, efficiency, and real-time performance. This technique is of particular significance in multimodal, sensor-fusion contexts where heterogeneity and uncertainty must be modeled explicitly.

A plausible implication is that further advances may extend this paradigm to multi-task fusion (e.g., combining segmentation and depth) or leveraging uncertainty for active perception systems in autonomy, opening avenues for robust generalization in both synthetic and in-the-wild scenarios.