Millions of species are currently being sequenced, and their genomes are being compared. Many of them have more complex genomes than model systems and raise novel challenges for genome alignment. Widely used local alignment strategies often produce limited or incongruous results when applied to genomes with dispersed repeats, long indels, and highly diverse sequences. Moreover, alignment using many-to-many or reciprocal best hit approaches conflicts with well-studied patterns between species with different rounds of whole-genome duplication. Here, we introduce Anchored Wavefront alignment (AnchorWave), which performs whole-genome duplication–informed collinear anchor identification between genomes and performs base pair–resolved global alignment for collinear blocks using a two-piece affine gap cost strategy. This strategy enables AnchorWave to precisely identify multikilobase indels generated by transposable element (TE) presence/absence variants (PAVs). When aligning two maize genomes, AnchorWave successfully recalled 87% of previously reported TE PAVs. By contrast, other genome alignment tools showed low power for TE PAV recall. AnchorWave precisely aligns up to three times more of the genome as position matches or indels than the closest competitive approach when comparing diverse genomes. Moreover, AnchorWave recalls transcription factor–binding sites at a rate of 1.05- to 74.85-fold higher than other tools with significantly lower false-positive alignments. AnchorWave complements available genome alignment tools by showing obvious improvement when applied to genomes with dispersed repeats, active TEs, high sequence diversity, and whole-genome duplication variation.