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Specifically, we utilize the nonequispaced fast Fourier transform to accelerate the radial kernel convolution in unbalanced optimal transport approximation, built upon the Sinkhorn algorithm. We also present accelerated schemes for maximum mean discrepancies involving kernels. Our approaches reduce the arithmetic operations needed to compute distances from <jats:inline-formula><jats:alternatives><jats:tex-math>$${{\\mathcal {O}}}\\left( n^{2}\\right) $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mfenced>\n                      <mml:msup>\n                        <mml:mi>n<\/mml:mi>\n                        <mml:mn>2<\/mml:mn>\n                      <\/mml:msup>\n                    <\/mml:mfenced>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> to <jats:inline-formula><jats:alternatives><jats:tex-math>$${{{\\mathcal {O}}}}\\left( n \\log n \\right) $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mfenced>\n                      <mml:mi>n<\/mml:mi>\n                      <mml:mo>log<\/mml:mo>\n                      <mml:mi>n<\/mml:mi>\n                    <\/mml:mfenced>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, opening the door to handle large and high-dimensional datasets efficiently. Furthermore, we establish robust connections between transportation problems, encompassing Wasserstein distance and unbalanced optimal transport, and maximum mean discrepancies. 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