Training-free controllable motion generation has attracted growing interest for enabling flexible constraint enforcement without constraint-specific training. However, existing training-free methods require constraints to be continuous objective-based with differentiable losses, while many real-world requirements are criterion-based and provide only discontinuous, sparse, or even black-box feedback. In this paper, we propose Motion-Inference-as-Control (MIC), the first training-free motion generation framework that handles both continuous objective-based and criterion-based motion constraints under a shared mechanism. The key idea is to cast diffusion-based motion generation as a stochastic control problem. This perspective not only provides principled and practically effective step-wise control laws that support criterion-based constraints without requiring differentiability and naturally accommodate objective-based constraints as a special case, but also motivates a control-oriented constraint coordination mechanism that adaptively balances and reconciles motion constraints during generation. Experiments across diverse constraint settings demonstrate the effectiveness of our framework.

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