Multidimensional Adaptive Coefficient for Inference Trajectory Optimization in Flow and Diffusion

Flow and diffusion models have demonstrated strong performance and training stability across various tasks but lack two critical properties of simulation-based methods: freedom of dimensionality and adaptability to different inference trajectories. To address this limitation, we propose the Multidimensional Adaptive Coefficient (MAC), a plug-in module for flow and diffusion models that extends conventional unidimensional coefficients to multidimensional ones and enables inference trajectory-wise adaptation. MAC is trained via simulation-based feedback through adversarial refinement. Empirical results across diverse frameworks and datasets demonstrate that MAC enhances generative quality with high training efficiency. Consequently, our work offers a new perspective on inference trajectory optimality, encouraging future research to move beyond vector field design and to leverage training-efficient, simulation-based optimization.

Consider the drawing process of a horse: we might first clarify the head, then refine the body—illustrating "Multidimensionality." For other animals, like a frog, it might be better to draw the body first, then complete the head—illustrating "Adaptability." Our research asks: which multidimensional adaptive inference trajectories yield the best generation quality?To answer this, we propose the Multidimensional Adaptive Coefficient (MAC), a plug-in module for flow and diffusion frameworks—standard tools in generative modeling. Across diverse frameworks and datasets, MAC discovers optimal inference trajectories, significantly improving generation quality and inference efficiency while achieving strong training efficiency.Our findings enhance generative modeling and offer a new perspective on inference trajectory optimality by enabling flexibility in multidimensionality and adaptability.