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Fonts are integral to creative endeavors, design processes, and artistic productions. The appropriate selection of a font can significantly enhance artwork and endow advertisements with a higher level of expressivity. Despite the availability of numerous diverse font designs online, traditional retrieval-based methods for font selection are increasingly being supplanted by generation-based approaches. These newer methods offer enhanced flexibility, catering to specific user preferences and capturing unique stylistic impressions. However, current impression font techniques based on Generative Adversarial Networks (GANs) necessitate the utilization of multiple auxiliary losses to provide guidance during generation. Furthermore, these methods commonly employ weighted summation for the fusion of impression-related keywords. This leads to generic vectors with the addition of more impression keywords, ultimately lacking in detail generation capacity. In this paper, we introduce a diffusion-based method, termed \ourmethod, to generate fonts that vividly embody specific impressions, utilizing an input consisting of a single letter and a set of descriptive impression keywords. The core innovation of \ourmethod lies in the development of dual cross-attention modules, which process the characteristics of the letters and impression keywords independently but synergistically, ensuring effective integration of both types of information. Our experimental results, conducted on the MyFonts dataset, affirm that this method is capable of producing realistic, vibrant, and high-fidelity fonts that are closely aligned with user specifications. This confirms the potential of our approach to revolutionize font generation by accommodating a broad spectrum of user-driven design requirements. Our code is publicly available at \url{https://github.com/leitro/GRIF-DM}., Comment: Accepted to ECAI2024