Multistep Consistency Models (MCMs) combine Consistency Models (Song et al., 2023) and TRACT (Berthelot et al., 2023), offering a trade-off between sampling speed and quality. MCMs allow for multiple steps in the sampling process, interpolating between consistency models (1-step) and diffusion models (infinite steps). By increasing the number of sampling steps, MCMs can generate higher quality samples while maintaining faster sampling speeds. The paper demonstrates that MCMs can achieve performance comparable to standard diffusion models with as few as 8 steps, achieving FID scores of 1.4 on ImageNet64 and 2.1 on ImageNet128. The paper introduces a deterministic sampler, aDDIM, which corrects for the integration error in DDIM, leading to improved sample quality. MCMs are trained using a loss function that generalizes consistency training and distillation, allowing for a more flexible and efficient training process. The method is shown to scale to text-to-image diffusion models, generating samples that match the quality of the original model. The paper also discusses the limitations of MCMs, including the increased computational cost due to multiple function evaluations. However, the trade-off between sample quality and speed is favorable, with MCMs achieving performance comparable to standard diffusion models with fewer steps. The results show that MCMs can be trained effectively from pre-trained diffusion models, leading to faster convergence and better performance. The paper compares MCMs with other methods, including adversarial distillation and consistency trajectory models, and shows that MCMs achieve better performance with fewer steps and without the need for adversarial training. The experiments on ImageNet and text-to-image models demonstrate the effectiveness of MCMs, with significant improvements in FID scores and sample quality. The results indicate that MCMs provide a promising approach for balancing sampling speed and quality in diffusion models.Multistep Consistency Models (MCMs) combine Consistency Models (Song et al., 2023) and TRACT (Berthelot et al., 2023), offering a trade-off between sampling speed and quality. MCMs allow for multiple steps in the sampling process, interpolating between consistency models (1-step) and diffusion models (infinite steps). By increasing the number of sampling steps, MCMs can generate higher quality samples while maintaining faster sampling speeds. The paper demonstrates that MCMs can achieve performance comparable to standard diffusion models with as few as 8 steps, achieving FID scores of 1.4 on ImageNet64 and 2.1 on ImageNet128. The paper introduces a deterministic sampler, aDDIM, which corrects for the integration error in DDIM, leading to improved sample quality. MCMs are trained using a loss function that generalizes consistency training and distillation, allowing for a more flexible and efficient training process. The method is shown to scale to text-to-image diffusion models, generating samples that match the quality of the original model. The paper also discusses the limitations of MCMs, including the increased computational cost due to multiple function evaluations. However, the trade-off between sample quality and speed is favorable, with MCMs achieving performance comparable to standard diffusion models with fewer steps. The results show that MCMs can be trained effectively from pre-trained diffusion models, leading to faster convergence and better performance. The paper compares MCMs with other methods, including adversarial distillation and consistency trajectory models, and shows that MCMs achieve better performance with fewer steps and without the need for adversarial training. The experiments on ImageNet and text-to-image models demonstrate the effectiveness of MCMs, with significant improvements in FID scores and sample quality. The results indicate that MCMs provide a promising approach for balancing sampling speed and quality in diffusion models.