Pulsatile physiological signals, characterized by rhythmic fluctuations, are vital for assessing health conditions and are widely used in wellness devices and medical equipment. Despite their significance, models addressing domain-specific unmet needs and considerations have not been developed as much as in other fields. Therefore, building on the foundation of variational autoencoders, we introduce VABAM, a novel model for the amplitude-based synthesis of pulsatile physiological signals. The uniqueness of VABAM lies in its ability to maintain the morphological identity of signals throughout the synthesis process, achieved by integrating pass filter effects within the variational autoencoder architecture. To assess the effectiveness of the model, we developed three novel metrics based on joint mutual information. These metrics were aimed at evaluating the disentanglement of latent spaces, influence of ancillary information on signal morphologies, and controllability of amplitude-based synthesis within morphological identities. Comparative analyses demonstrated that VABAM and its variants were notably effective at preserving morphological integrity, highlighting their potential to minimize morphological distortions in physiological signal processing and their compatibility with artificial intelligence models employing frequency and amplitude features. Additionally, the proposed metrics, compatible with probabilistic models, were empirically proven to capture the characteristics of various models from multiple perspectives.