Simulating physically plausible trajectories toward user-defined goals is a fundamental yet challenging task in fluid dynamics. While particle-based simulators can efficiently reproduce forward dynamics, inverse inference remains difficult, especially in dissipative systems where dynamics are irreversible and optimization-based solvers are slow, unstable, and often fail to converge. In this work, we introduce the Reversible Graph Network Simulator (R-GNS), a unified framework that enforces bidirectional consistency within a single graph architecture. Unlike prior neural simulators that approximate inverse dynamics by fitting backward data, R-GNS does not attempt to reverse the underlying physics. Instead, we propose a mathematically invertible design based on residual reversible message passing with shared parameters, coupling forward dynamics with inverse inference to deliver accurate predictions and efficient recovery of plausible initial states. Experiments on three dissipative benchmarks (Water-3D, WaterRamps, and WaterDrop) show that R-GNS achieves higher accuracy and consistency with only one quarter of the parameters, and performs inverse inference more than 100 times faster than optimization-based baselines. For forward simulation, R-GNS matches the speed of strong GNS baselines, while in goal-conditioned tasks it eliminates iterative optimization and achieves orders-of-magnitude speedups. On goal-conditioned tasks, R-GNS further demonstrates its ability to complex target shapes (e.g., characters "L" and "N") through vivid, physically consistent trajectories. To our knowledge, this is the first reversible framework that unifies forward and inverse simulation for dissipative fluid systems.