Abstract
Parameter landscapes of biological dynamical systems are notoriously difficult to interpret: they are high-dimensional, expensive to explore through simulation, and organized by bifurcations that partition parameter space into regimes with qualitatively distinct dynamics. Consequently, local optimization and low-dimensional parameter sweeps often miss large portions of the viable parameter set and obscure how robustness emerges through interactions among parameters. I present a score-based diffusion framework that learns conditional distributions concentrated near *viable parameter manifolds*, enabling efficient exploration beyond the dimensionality accessible to exhaustive sweeps. We begin by randomly sampling parameter values and summarizing the long-term behaviors obtained from model simulations. Conditioned on prescribed target behaviors, the diffusion model then generates new parameter values concentrated near the corresponding viable set. We characterize the local geometry of these sets through their intrinsic dimension, tangent spaces, and curvature. These quantities reveal mechanistic properties such as effective degrees of freedom, compensatory parameter directions, and higher-order interactions that collectively shape system behavior.
Our results span three dynamical systems: the Lorenz system, the Izhikevich neuron model, and dsODE, our reduced ODE description of spiking neural network dynamics. We identify and analyze viable parameter manifolds in ambient parameter spaces of up to 12 dimensions. Across these examples, generative learning provides a principled and scalable framework for relating parameter-space geometry to mechanism, compensation, and robustness in complex biological models.