Rendering dynamic reverberation in a complicated acoustic space for moving sources and listeners is challenging but crucial for enhancing user immersion in extended-reality (XR) applications. Capturing spatially varying room impulse responses (RIRs) is costly and often impractical. Moreover, dynamic convolution with measured RIRs is computationally expensive with high memory demands, typically not available on wearable computing devices. Grouped Feedback Delay Networks (GFDNs), on the other hand, allow efficient rendering of coupled room acoustics. However, its parameters need to be tuned to match the reverberation profile of a coupled space. In this work, we propose the concept of Differentiable GFDNs (DiffGFDNs), which have tunable parameters that are optimised to match the late reverberation profile of a set of RIRs captured from a space that exhibits multi-slope decay. Once trained on a finite set of measurements, the DiffGFDN interpolates to unmeasured locations in the space. We propose a parallel processing pipeline that has multiple DiffGFDNs with frequency-independent parameters processing each octave band. The parameters of the DiffGFDN can be updated rapidly during inferencing as sources and listeners move. We evaluate the proposed architecture against the Common Slopes (CS) model on a dataset of RIRs for three coupled rooms. The proposed architecture generates multi-slope late reverberation with low memory and computational requirements, achieving a better energy decay relief (EDR) error and slightly worse octave-band energy decay curve (EDC) errors compared to the CS model. Furthermore, DiffGFDN requires an order of magnitude fewer floating-point operations per sample than the CS renderer.