where 𝑄 6 / , 𝑄 1 / and 𝑄 7 / are transition matrices for the categorical distributions to 𝐴, 𝐶 and 𝐸, as described in ref 21. The denoising model of MIDI is a Transformer model, consisting of 12 equivariant graph transformer (E3-GT) blocks, as depicted in Figure . The first six of these blocks function as the encoder, and the latter half as the decoder. As demonstrated in Figure , each E3-GT block processes 3D molecular graph data 𝐺 = {𝐴, 𝐶, 𝐸, 𝑅, ℊ}, and performs a sequence of internal operations to update the graph's features. These operations include the extraction of 3D information, updating of edge (𝐸) and node features (𝑉 = 𝐴⨁𝐶), R coordinates with rEGNN 29 ,and graph embeddings (ℊ), followed by drop-out and normalization steps, which are detailed in Figure . The coordinate updating relies on distances between atoms, which preserves the E3 equivariance of the graph.