Accurate prediction and synthesis of seismic waveforms are crucial for seismic-hazard assessment and earthquake-resistant infrastructure design. Existing prediction methods, such as ground-motion models and physics-based wave-field simulations, often fail to capture the full complexity of seismic wavefields, particularly at higher frequencies. This study introduces HighFEM, a novel, computationally efficient, and scalable (i.e., capable of generating many seismograms simultaneously) generative model for high-frequency seismic-waveform generation. Our approach leverages a spectrogram representation of the seismic-waveform data, which is reduced to a lower-dimensional manifold via an autoencoder. A state-of-the-art diffusion model is trained to generate this latent representation conditioned on key input parameters: earthquake magnitude, recording distance, site conditions, hypocenter depth, and azimuthal gap. The model generates waveforms with frequency content up to 50 Hz. Any scalar ground-motion statistic, such as peak ground-motion amplitudes and spectral accelerations, can be readily derived from the synthesized waveforms. We validate our model using commonly employed seismological metrics and performance metrics from image-generation studies. Our results demonstrate that the openly available model can generate realistic high-frequency seismic waveforms across a wide range of input parameters, even in data-sparse regions. For the scalar ground-motion statistics commonly used in seismic-hazard and earthquake-engineering studies, we show that our model accurately reproduces both the median trends of the real data and their variability. To evaluate and compare the growing number of these and similar Generative Waveform Models (GWMs), we argue that they should be openly available and included in community ground-motion-model evaluation efforts.