Non-convex optimization in high dimensions requires balancing gradient information with global exploration, a tension that Langevin dynamics and other gradient-informed methods address only partially. We introduce a gradient-based swarm method driven by a Softmin Energy interaction $J_\beta(\mathbf{x})$, a smooth approximation of the per-particle minimum that couples particles through their relative energies. Combining the resulting gradient flow with Brownian noise and an annealing schedule on $\beta$, we obtain a dynamics that retains the efficiency of gradient steps while inheriting the global-search behavior of swarm methods. Our main theoretical result is an Eyring-Kramers-type estimate showing that the effective potential barriers are strictly smaller than those of overdamped Langevin dynamics, yielding provably faster transitions between local minima. Numerical experiments on double-well and high-dimensional Ackley benchmarks confirm the analysis and show improved convergence over Simulated Annealing, Gradient-Enhanced Particle Swarm Optimization, and Gradient-Aware Consensus Based Optimization.