In recent years, generative adversarial networks (GANs) have made significant progress in generating audio sequences. However, these models typically rely on bandwidth-limited mel-spectrograms, which constrain the resolution of generated audio sequences, and lead to mode collapse during conditional generation. To address this issue, we propose Deformable Periodic Network based GAN (DPN-GAN), a novel GAN architecture that incorporates a kernel-based periodic ReLU activation function to induce periodic bias in audio generation. This innovative approach enhances the model's ability to capture and reproduce intricate audio patterns. In particular, our proposed model features a DPN module for multi-resolution generation utilizing deformable convolution operations, allowing for adaptive receptive fields that improve the quality and fidelity of the synthetic audio. Additionally, we enhance the discriminator network using deformable convolution to better distinguish between real and generated samples, further refining the audio quality. We trained two versions of the model: DPN-GAN small (38.67M parameters) and DPN-GAN large (124M parameters). For evaluation, we use five different datasets, covering both speech synthesis and music generation tasks, to demonstrate the efficiency of the DPN-GAN. The experimental results demonstrate that DPN-GAN delivers superior performance on both out-of-distribution and noisy data, showcasing its robustness and adaptability. Trained across various datasets, DPN-GAN outperforms state-of-the-art GAN architectures on standard evaluation metrics, and exhibits increased robustness in synthesized audio.