In this paper, we present Interstellar, a novel folding and IVC framework built on a technique we call circuit interpolation, tailored for circuit satisfiability. By incorporating the GKR protocol, our approach avoids commitments to full computation traces and cross-term vectors, requiring instead only commitments to the actual circuit witness and optionally a small subset of intermediate gate values. This substantially reduces the size of the vectors to be committed to in each folding round, which is highly advantageous compared to existing schemes, as vector commitments involve expensive multi-scalar multiplications. We evaluate Interstellar using two representative workloads: product of matrices which models highly parallel computation, and MiMC hash chains which captures highly serialized computation. Our analysis shows that Interstellar achieves 1.59x to 6.74x prover speedup per folding round for matrix multiplication and up to 2.93x speedups for MiMC chains compared to alternative methods. Beyond efficiency, Interstellar is highly flexible. It can be extended to support high-degree and lookup gates, multi-instance folding, and non-uniform IVC, making it well-suited for practical applications such as zkML and zkVM. Finally, we formalize, for the first time, a new notion called collaborative folding/IVC, which allows folding/IVC proof generation with multiple provers holding disjoint private witnesses for the same public statement. This new primitive enables distributed IVC proof generation while preserving witness privacy across folding rounds, making Interstellar a compelling fit for distributed and privacy-sensitive applications.