Sign language production (SLP) aims to translate spoken language sentences into a sequence of pose frames in a sign language, bridging the communication gap and promoting digital inclusion for deaf and hard-of-hearing communities. Existing methods typically rely on gloss, a symbolic representation of sign language words or phrases that serves as an intermediate step in SLP. This limits the flexibility and generalization of SLP, as gloss annotations are often unavailable and language-specific. Therefore, we present a novel diffusion-based generative approach - Text2Sign Diffusion (Text2SignDiff) for gloss-free SLP. Specifically, a gloss-free latent diffusion model is proposed to generate sign language sequences from noisy latent sign codes and spoken text jointly, reducing the potential error accumulation through a non-autoregressive iterative denoising process. We also design a cross-modal signing aligner that learns a shared latent space to bridge visual and textual content in sign and spoken languages. This alignment supports the conditioned diffusion-based process, enabling more accurate and contextually relevant sign language generation without gloss. Extensive experiments on the commonly used PHOENIX14T and How2Sign datasets demonstrate the effectiveness of our method, achieving the state-of-the-art performance.