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*Diffusion-based purification* (DBP) methods aim to remove adversarial noise from the input sample by first injecting Gaussian noise through a forward diffusion process, and then recovering the clean example through a reverse generative process. In the above process, how much Gaussian noise is injected to the input sample is key to the success of DBP methods, which is controlled by a constant noise level $t*$ for all samples in existing methods. In this paper, we discover that an optimal $t*$ for each sample indeed could be different. Intuitively, the cleaner a sample is, the less the noise it should be injected, and vice versa. Motivated by this finding, we propose a new framework, called Sample-specific Score-aware Noise Injection (SSNI). Specifically, SSNI uses a pre-trained score network to estimate how much a data point deviates from the clean data distribution (i.e., score norms). Then, based on the magnitude of score norms, SSNI applies a reweighting function to adaptively adjust $t*$ for each sample, achieving sample-specific noise injections. Empirically, incorporating our framework with existing DBP methods results in a notable improvement in both accuracy and robustness on CIFAR-10 and ImageNet-1K, highlighting the necessity to allocate *distinct noise levels to different samples* in DBP methods. Our code is available at: https://github.com/tmlr-group/SSNI.