Generative modeling frameworks have emerged as an effective approach to capture high-dimensional image distributions from large datasets without requiring domain-specific knowledge, a capability essential for longitudinal disease progression modeling. Recent generative modeling approaches have attempted to capture progression by mapping images into a latent representational space and then controlling and guiding the representations to generate follow-up images from a baseline image. However, existing approaches impose constraints on distribution learning, leading to latent spaces with limited controllability to generate follow-up images without explicit supervision from subject-specific longitudinal images. In order to enable controlled movements in the latent representational space and generate progression images from a baseline image in an unsupervised manner, we introduce a conditionable Diffusion Auto-encoder framework. The explicit encoding mechanism of image-diffusion auto-encoders forms a compact latent space capturing high-level semantics, providing means to disentangle information relevant for progression. Our approach leverages this latent space to condition and apply controlled shifts to baseline representations for generating follow-up. Controllability is induced by restricting these shifts to a subspace, thereby isolating progression-related factors from subject identity-preserving components. The shifts are implicitly guided by correlating with progression attributes, without requiring subject-specific longitudinal supervision. We validate the generations through image quality metrics, volumetric progression analysis, and downstream classification in Alzheimer's disease datasets from two different sources and disease categories. This demonstrates the effectiveness of our approach for Alzheimer's progression modeling and longitudinal image generation.