Instrumentation is vital to fuzzing. It provides fuzzing directions and helps detect covert bugs, yet its overhead greatly reduces the fuzzing throughput. To reduce the overhead, compilers compromise instrumentation correctness for better optimization, or seek convoluted runtime support to remove unused probes during fuzzing. In this paper, we propose Odin, an on-demand instrumentation framework to instrument C/C++ programs correctly and flexibly. When instrumentation requirement changes during fuzzing, Odin first locates the changed code fragment, then re-instruments, re-optimizes, and re-compiles the small fragment on-the-fly. Consequently, with a minuscule compilation overhead, the runtime overhead of unused probes is annihilated. Its architecture design ensures correctness in instrumentation, optimized code generation, and low latency in recompilation. Experiments show that the Odin delivers the performance of compiler-based static instrumentation while retaining the flexibility of binary-based dynamic instrumentation. When applied for coverage instrumentation, Odin’s coverage collection is 3× faster than LLVM SanitizerCoverage and 17× faster than DynamoRIO.