Reconstructing volumetric smoke from 2D images remains challenging in computer graphics. Although physics-based differentiable rendering offers a promising solution, existing methods are computationally expensive and impractical for interactive use. We introduce an efficient physics-based differentiable renderer tailored for smoke reconstruction, based on two insights: (ⅰ) for the optically thin-to-moderately dense smoke targeted in this work, appearance is well approximated by single scattering, allowing us to avoid costly multiple-scattering simulation, and (ⅱ) direction-independent terms can be precomputed to avoid redundant forward and backward passes. Our technical contributions include a pre-computation strategy that eliminates repetitive calculations, and an efficient ray marching method that computes density derivatives without costly Monte Carlo estimation or automatic differentiation. Comprehensive evaluation shows that our approach achieves real-time performance while maintaining high reconstruction quality. In contrast to current best methods that require minutes per frame, our method enables interactive smoke reconstruction while maintaining competitive visual fidelity. We demonstrate its utility in applications such as augmented reality and fluid motion reconstruction.