This paper proposes Diffusion with Spherical Gaussian Constraint (DSG), a novel training-free method for conditional diffusion models. The key issue addressed is the manifold deviation during the sampling process when using loss guidance. The authors theoretically show that this deviation is caused by the Jensen gap, which increases with the number of sample dimensions. To mitigate this, DSG introduces a spherical Gaussian constraint that restricts the guidance step within the intermediate data manifold, enabling larger step sizes and improving sample quality and efficiency. DSG is designed as a plug-and-play module that can be integrated into existing training-free conditional diffusion models with minimal computational overhead. The method is validated through experiments on various conditional generation tasks, demonstrating significant performance improvements in both sample quality and time efficiency. However, DSG may compromise sample diversity by restricting Gaussian sampling to the gradient descent direction. The paper also discusses the theoretical foundations of DSG, including the concentration phenomenon in high-dimensional Gaussian distributions and the use of closed-form solutions for denoising. The results show that DSG outperforms existing training-free methods in terms of both quality and efficiency, while maintaining compatibility with a wide range of conditional generation tasks.This paper proposes Diffusion with Spherical Gaussian Constraint (DSG), a novel training-free method for conditional diffusion models. The key issue addressed is the manifold deviation during the sampling process when using loss guidance. The authors theoretically show that this deviation is caused by the Jensen gap, which increases with the number of sample dimensions. To mitigate this, DSG introduces a spherical Gaussian constraint that restricts the guidance step within the intermediate data manifold, enabling larger step sizes and improving sample quality and efficiency. DSG is designed as a plug-and-play module that can be integrated into existing training-free conditional diffusion models with minimal computational overhead. The method is validated through experiments on various conditional generation tasks, demonstrating significant performance improvements in both sample quality and time efficiency. However, DSG may compromise sample diversity by restricting Gaussian sampling to the gradient descent direction. The paper also discusses the theoretical foundations of DSG, including the concentration phenomenon in high-dimensional Gaussian distributions and the use of closed-form solutions for denoising. The results show that DSG outperforms existing training-free methods in terms of both quality and efficiency, while maintaining compatibility with a wide range of conditional generation tasks.