Final answer:
The process most directly related to the cell theory's statement that new cells come from existing cells is Cell Division. This is in line with observations made by scientists such as Rudolf Virchow and is an essential aspect of the cell cycle.
Step-by-step explanation:
The cellular process most directly related to the statement "New cells are produced from existing cells" in the cell theory is Cell Division. The cell theory is one of the fundamental theories of biology and it includes the concept that all living organisms are made from cells and that these cells arise from pre-existing cells. This principle was proposed by scientists including Rudolf Virchow, who, after studying cells under a microscope, observed them dividing and forming new cells, leading to the conclusion that living cells can only arise from other living cells.
During the cell cycle, a cell grows, replicates its DNA, and then divides into two new daughter cells through a process known as mitosis (in eukaryotic cells) or binary fission (in prokaryotic cells). This process is crucial for growth, repair, and reproduction in all living organisms. Other options like differentiation, growth, and regulation are important in the life of a cell but division is the process that directly leads to the production of new cells from existing ones in accordance with the cell theory.
Therefore, the final answer, in a two line explanation in 300 words: Cell Division is most directly related to the production of new cells from existing cells, emphasizing the cell theory's tenet that cells can only arise from other living cells through the cell cycle.