This paper proposes a new compression paradigm -- Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) -- for lossy scientific data compression. The framework is based on recent conditional diffusion (CD) generative models, and it consists of a conditional diffusion model, tensor correction, and error guarantee. Our diffusion model is a mixture of 3D conditioning and 2D denoising U-Net. The approach leverages a 3D block-based compressing module to address spatiotemporal correlations in structured scientific data. Then, the reverse diffusion process for 2D spatial data is conditioned on the ``slices'' of content latent variables produced by the compressing module. After training, the denoising decoder reconstructs the data with zero noise and content latent variables, and thus it is entirely deterministic. The reconstructed outputs of the CD model are further post-processed by our tensor correction and error guarantee steps to control and ensure a maximum error distortion, which is an inevitable requirement in lossy scientific data compression. Our experiments involving two datasets generated by climate and chemical combustion simulations show that our framework outperforms standard convolutional autoencoders and yields competitive compression quality with an existing scientific data compression algorithm.