Diffusion models are predominantly built on Gaussian perturbations, whose symmetry and light-tailed behavior provide substantial analytical and algorithmic convenience. However, this design choice can be restrictive when the target perturbation structure is asymmetric, skewed, or exhibits localized abrupt variations. We present Gamma-Noise Diffusion Models (GNDM), a non-Gaussian diffusion framework that replaces Gaussian perturbations with gamma-driven increments while preserving the familiar score-based training and reverse-time sampling interface. Our approach constructs a forward corruption process with composable gamma perturbations, derives an approximate reverse-time stochastic dynamics using a local expansion of the reverse conditional, and further develops a probability-flow ordinary differential equation (ODE) that enables deterministic sampling. We also introduce a weighted score-matching objective adapted to the conditional gamma perturbation family. Experiments on MNIST, CIFAR-10, and CelebA demonstrate that the proposed framework is practically trainable and capable of high-quality generation. On unconditional CIFAR-10 generation, our implementation achieves an FID of 2.58 and an IS of 10.02. These results suggest that diffusion modeling can be extended beyond Gaussian assumptions without discarding the core score-based generative modeling pipeline.