ResearchPod Summary
Standard diffusion models are excellent at capturing data distributions but often fail to satisfy complex, task-specific feasibility constraints (e.g., collision avoidance in robotics or staying on-road in autonomous driving). Existing methods either enforce constraints during training—which suffers from a mismatch between training and sampling states—or during inference, which can introduce distribution shift and instability, especially when using few-step sampling. This paper asks: can we align the training process with the actual denoising trajectory to improve constraint satisfaction without sacrificing sample quality?
To bridge the gap between training and inference, the authors propose Integration Matters for Constrained Diffusion (IMCD). Instead of training on forward-noised states, IMCD performs online denoising rollouts during training. By differentiating through the fixed noise schedule used for numerical integration, the model is exposed to the specific infeasible states it encounters during sampling. The framework uses a learnable scaling network that adapts guidance strength dynamically based on the current state and noise level, eliminating the need for manual hyperparameter tuning. The final training objective combines a standard denoising loss (to maintain data fidelity) with a terminal rollout constraint loss (to enforce feasibility).
Theoretical analysis confirms that backpropagating through the rollout computes the exact gradient of the constraint objective under the model's own sampling distribution. Empirical experiments on bouncing ball trajectories and traffic scene prediction demonstrate that IMCD significantly improves constraint satisfaction compared to prior fine-tuning and sampling-time correction methods. Furthermore, the learned scaling mechanism ensures that the model remains stable and maintains high-quality generation even when using few-step sampling, where previous methods often struggle with distribution shift.
This work provides a robust way to deploy generative models in safety-critical environments. By ensuring that the model learns to correct itself along the path it actually takes during inference, IMCD offers a more reliable alternative to post-hoc guidance, which often forces the model into low-probability regions of the data manifold.
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