<p>We continue our investigation on denominator conjecture of Fomin and Zelevinsky for cluster algebras via geometric models initialed in Fu and Geng (Intersection vectors over tilings with applications to gentle algebras and cluster algebras. <a href="http://arxiv.org/abs/2212.11497">arXiv:2212.11497</a>, 2022). In this paper, we confirm the denominator conjecture for cluster algebras of finite type. Our main contribution is a proof of this conjecture for cluster algebras of type <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">D</mi> </math></EquationSource> </InlineEquation>, along with an algorithm for the exceptional types. For the type <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">D</mi> </math></EquationSource> </InlineEquation> cases, our approach involves a geometric model based on discs with a puncture. By removing the puncture or changing it to an unmarked boundary component, we also provide an alternative proof of the denominator conjecture for cluster algebras of types <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {A}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">A</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">C</mi> </math></EquationSource> </InlineEquation>, respectively.</p>