Diffusion fashions (DMs) have just lately emerged as SoTA instruments for generative modeling in numerous domains. Normal DMs might be seen as an instantiation of hierarchical variational autoencoders (VAEs) the place the latent variables are inferred from input-centered Gaussian distributions with mounted scales and variances. Not like VAEs, this formulation constrains DMs from altering the latent areas and studying summary representations. On this work, we suggest f-DM, a generalized household of DMs which permits progressive sign transformation. Extra exactly, we prolong DMs to include a set of (hand-designed or realized) transformations, the place the reworked enter is the imply of every diffusion step. We suggest a generalized formulation and derive the corresponding de-noising goal with a modified sampling algorithm. As an illustration, we apply f-DM in picture technology duties with a spread of capabilities, together with down-sampling, blurring, and realized transformations based mostly on the encoder of pretrained VAEs. As well as, we determine the significance of adjusting the noise ranges every time the sign is sub-sampled and suggest a easy rescaling recipe. f-DM can produce high-quality samples on normal picture technology benchmarks like FFHQ, AFHQ, LSUN, and ImageNet with higher effectivity and semantic interpretation.