Existing product design methods have certain limitations in terms of creative generation and optimization, especially in the realization of creative diversity and cross-modal design. To solve these problems, this paper proposes a product innovation design model based on generative adversarial networks (GANs). This model uses the adversarial mechanism between the generator and the discriminator to achieve diversified creative generation, explore the design potential space, and realize the transformation from two-dimensional images to three-dimensional models through cross-modal design. At the same time, multi-objective optimization algorithms are used to comprehensively consider multiple optimization objectives such as function, appearance, cost and producibility in the design to enhance the market competitiveness of the design. Through the evaluation and feedback mechanism, user feedback is combined with design testing to ensure that the generated design not only meets the expected goals, but can also be verified in practical applications. The research in this paper shows that the total cost of sample 2 and sample 5 is 300,000 yuan and 280,000 yuan, respectively, which is the lowest among all samples. And their cost-effectiveness ratio is also relatively good, 3.46 and 3.23, respectively. It shows that these two designs have outstanding performance in cost control and have achieved a good balance in design quality. The product innovation design model based on GAN can significantly improve the efficiency and quality of creative generation and promote the intelligence and optimization of product design process.