(048.96, 763.44) (059.81, 763.44) (059.81, 772.08) (048.96, 772.08)      /F115 LIU	<|special_separator|>
(061.75, 763.95) (076.87, 763.95) (076.87, 770.39) (061.75, 770.39)      /F140 et al.	<|special_separator|>
(076.87, 763.44) (338.23, 763.44) (338.23, 772.08) (076.87, 772.08)      /F115 : PREPARATION OF PAPERS FOR IEEE TRANSACTIONS ON MEDICAL IMAGING	<|special_separator|>
(559.15, 763.44) (563.03, 763.44) (563.03, 772.08) (559.15, 772.08)      /F115 3	<|special_separator|>
(094.74, 728.67) (177.36, 728.67) (177.36, 734.53) (094.74, 734.53)     /Font0 Source MRIs and Treatments	<|special_separator|>
(380.81, 728.67) (395.63, 728.67) (395.63, 734.53) (380.81, 734.53)     /Font0 MRIs	<|special_separator|>
(463.94, 728.67) (502.19, 728.67) (502.19, 734.53) (463.94, 734.53)     /Font0 Tumor masks	<|special_separator|>
(094.74, 718.91) (101.45, 718.91) (101.45, 724.75) (094.74, 724.75)     /Font1 s1	<|special_separator|>
(132.63, 718.91) (139.35, 718.91) (139.35, 724.75) (132.63, 724.75)     /Font1 s2	<|special_separator|>
(170.53, 718.91) (177.25, 718.91) (177.25, 724.75) (170.53, 724.75)     /Font1 s3	<|special_separator|>
(203.95, 718.89) (220.20, 718.89) (220.20, 724.75) (203.95, 724.75)     /Font0 Noise	<|special_separator|>
(387.33, 718.91) (389.09, 718.91) (389.09, 724.75) (387.33, 724.75)     /Font1 f	<|special_separator|>
(425.22, 718.91) (426.99, 718.91) (426.99, 724.75) (425.22, 724.75)     /Font1 f	<|special_separator|>
(460.68, 718.91) (467.39, 718.91) (467.39, 724.75) (460.68, 724.75)     /Font1 s3	<|special_separator|>
(498.57, 718.91) (505.29, 718.91) (505.29, 724.75) (498.57, 724.75)     /Font1 s2	<|special_separator|>
(536.47, 718.91) (543.19, 718.91) (543.19, 724.75) (536.47, 724.75)     /Font1 s1	<|special_separator|>
(070.61, 694.85) (078.03, 694.85) (078.03, 700.71) (070.61, 700.71)     /Font0 T1	<|special_separator|>
(067.44, 656.13) (078.03, 656.13) (078.03, 662.00) (067.44, 662.00)     /Font0 T1c	<|special_separator|>
(416.67, 663.36) (549.80, 663.36) (549.80, 669.22) (416.67, 669.22)     /Font0 Segmentations on both future and source MRIs	<|special_separator|>
(423.19, 648.74) (542.91, 648.74) (542.91, 654.61) (423.19, 654.61)     /Font0 Uncertainties on segmented tumor regions	<|special_separator|>
(065.67, 617.42) (078.03, 617.42) (078.03, 623.28) (065.67, 623.28)     /Font0 Flair	<|special_separator|>
(049.31, 593.38) (078.26, 593.38) (078.26, 599.24) (049.31, 599.24)     /Font0 Treatment	<|special_separator|>
(091.88, 593.40) (104.94, 593.40) (104.94, 599.24) (091.88, 599.24)     /Font1 CRT	<|special_separator|>
(129.38, 593.40) (142.43, 593.40) (142.43, 599.24) (129.38, 599.24)     /Font1 TMZ	<|special_separator|>
(167.27, 593.40) (180.32, 593.40) (180.32, 599.24) (167.27, 599.24)     /Font1 TMZ	<|special_separator|>
(202.73, 588.51) (220.91, 588.51) (220.91, 594.35) (202.73, 594.35)     /Font1 T=600	<|special_separator|>
(291.56, 592.94) (304.61, 592.94) (304.61, 598.80) (291.56, 598.80)     /Font2 TMZ	<|special_separator|>
(400.77, 593.40) (413.82, 593.40) (413.82, 599.24) (400.77, 599.24)     /Font1 TMZ	<|special_separator|>
(457.42, 593.40) (470.47, 593.40) (470.47, 599.24) (457.42, 599.24)     /Font1 TMZ	<|special_separator|>
(495.31, 593.40) (508.37, 593.40) (508.37, 599.24) (495.31, 599.24)     /Font1 TMZ	<|special_separator|>
(533.62, 593.40) (546.68, 593.40) (546.68, 599.24) (533.62, 599.24)     /Font1 CRT	<|special_separator|>
(066.73, 583.60) (078.03, 583.60) (078.03, 589.46) (066.73, 589.46)     /Font0 Day	<|special_separator|>
(094.74, 583.62) (101.81, 583.62) (101.81, 589.46) (094.74, 589.46)     /Font1 36	<|special_separator|>
(132.63, 583.62) (139.70, 583.62) (139.70, 589.46) (132.63, 589.46)     /Font1 64	<|special_separator|>
(168.50, 583.62) (179.10, 583.62) (179.10, 589.46) (168.50, 589.46)     /Font1 127	<|special_separator|>
(292.78, 583.57) (303.39, 583.57) (303.39, 589.43) (292.78, 589.43)     /Font2 225	<|special_separator|>
(402.00, 583.60) (412.60, 583.60) (412.60, 589.46) (402.00, 589.46)     /Font2 255	<|special_separator|>
(458.64, 583.62) (469.24, 583.62) (469.24, 589.46) (458.64, 589.46)     /Font1 127	<|special_separator|>
(498.57, 583.62) (505.64, 583.62) (505.64, 589.46) (498.57, 589.46)     /Font1 64	<|special_separator|>
(536.47, 583.62) (543.54, 583.62) (543.54, 589.46) (536.47, 589.46)     /Font1 36	<|special_separator|>
(048.96, 560.01) (071.38, 560.01) (071.38, 569.88) (048.96, 569.88)      /F115 Fig. 1.	<|special_separator|>
(078.85, 560.01) (563.03, 560.01) (563.03, 569.88) (078.85, 569.88)      /F115 An overview of the TaDiff model (short for Treatment-aware Diffusion Probabilistic model). The goal of our method is to generate a set of	<|special_separator|>
(048.96, 551.05) (563.03, 551.05) (563.03, 560.91) (048.96, 560.91)      /F115 synthetic MRIs and tumor progression masks for any given target/future treatment (e.g., TMZ: temozolomide) and time point (e.g., Day: 225) with	<|special_separator|>
(048.96, 542.08) (153.83, 542.08) (153.83, 551.95) (048.96, 551.95)      /F115 source sequential MRIs (e.g.,	<|special_separator|>
(156.50, 542.65) (164.91, 542.65) (164.91, 550.03) (156.50, 550.03)      /F140 s1	<|special_separator|>
(164.91, 542.08) (167.13, 542.08) (167.13, 551.95) (164.91, 551.95)      /F115 ,	<|special_separator|>
(169.79, 542.65) (178.21, 542.65) (178.21, 550.03) (169.79, 550.03)      /F140 s2	<|special_separator|>
(178.21, 542.08) (196.38, 542.08) (196.38, 551.95) (178.21, 551.95)      /F115 , and	<|special_separator|>
(199.04, 542.65) (207.46, 542.65) (207.46, 550.03) (199.04, 550.03)      /F140 s3	<|special_separator|>
(207.89, 542.08) (563.03, 542.08) (563.03, 551.95) (207.89, 551.95)      /F115 ) and treatments (e.g., CRT: chemoradiation at Day 36, TMZ at Days 64 and 127). More details are	<|special_separator|>
(048.96, 533.11) (132.69, 533.11) (132.69, 542.98) (048.96, 542.98)      /F115 presented in Section III.	<|special_separator|>
(048.96, 499.38) (055.05, 499.38) (055.05, 507.93) (048.96, 507.93)      /F123 It	<|special_separator|>
(060.38, 499.38) (067.02, 499.38) (067.02, 507.93) (060.38, 507.93)      /F123 is	<|special_separator|>
(072.36, 499.38) (117.34, 499.38) (117.34, 507.93) (072.36, 507.93)      /F123 noteworthy	<|special_separator|>
(122.67, 499.38) (137.62, 499.38) (137.62, 507.93) (122.67, 507.93)      /F123 that	<|special_separator|>
(142.95, 499.38) (155.12, 499.38) (155.12, 507.93) (142.95, 507.93)      /F123 the	<|special_separator|>
(160.45, 499.38) (188.81, 499.38) (188.81, 507.93) (160.45, 507.93)      /F123 reverse	<|special_separator|>
(194.15, 499.38) (238.99, 499.38) (238.99, 507.93) (194.15, 507.93)      /F123 conditional	<|special_separator|>
(244.32, 499.38) (288.04, 499.38) (288.04, 507.93) (244.32, 507.93)      /F123 probability	<|special_separator|>
(293.37, 499.38) (300.02, 499.38) (300.02, 507.93) (293.37, 507.93)      /F123 is	<|special_separator|>
(048.96, 487.42) (172.31, 487.42) (172.31, 495.97) (048.96, 495.97)      /F123 tractable when conditioned on	<|special_separator|>
(175.79, 487.58) (181.84, 487.58) (181.84, 496.32) (175.79, 496.32)      /F128 x	<|special_separator|>
(181.84, 486.66) (185.81, 486.66) (185.81, 492.76) (181.84, 492.76)       /F23 0	<|special_separator|>
(186.31, 487.42) (189.08, 487.42) (189.08, 495.97) (186.31, 495.97)      /F123 :	<|special_separator|>
(084.15, 468.82) (088.59, 468.82) (088.59, 477.53) (084.15, 477.53)       /F27 q	<|special_separator|>
(088.95, 468.82) (092.83, 468.82) (092.83, 477.53) (088.95, 477.53)       /F24 (	<|special_separator|>
(092.83, 468.81) (098.87, 468.81) (098.87, 477.56) (092.83, 477.56)      /F128 x	<|special_separator|>
(098.87, 467.90) (101.88, 467.90) (101.88, 473.99) (098.87, 473.99)       /F26 t	<|special_separator|>
(101.88, 462.60) (108.11, 462.60) (108.11, 474.69) (101.88, 474.69)       /F29 -	<|special_separator|>
(108.11, 467.90) (112.08, 467.90) (112.08, 473.99) (108.11, 473.99)       /F23 1	<|special_separator|>
(112.58, 461.16) (115.35, 461.16) (115.35, 478.45) (112.58, 478.45)       /F30 |	<|special_separator|>
(115.35, 468.81) (121.39, 468.81) (121.39, 477.56) (115.35, 477.56)      /F128 x	<|special_separator|>
(121.39, 467.90) (124.40, 467.90) (124.40, 473.99) (121.39, 473.99)       /F26 t	<|special_separator|>
(124.90, 468.82) (127.67, 468.82) (127.67, 477.53) (124.90, 477.53)       /F27 ,	<|special_separator|>
(129.33, 468.81) (135.37, 468.81) (135.37, 477.56) (129.33, 477.56)      /F128 x	<|special_separator|>
(135.38, 467.90) (139.35, 467.90) (139.35, 473.99) (135.38, 473.99)       /F23 0	<|special_separator|>
(139.84, 468.82) (154.24, 468.82) (154.24, 477.53) (139.84, 477.53)       /F24 ) =	<|special_separator|>
(157.00, 461.16) (165.18, 461.16) (165.18, 478.45) (157.00, 478.45)       /F30 N	<|special_separator|>
(166.64, 468.82) (170.52, 468.82) (170.52, 477.53) (166.64, 477.53)       /F24 (	<|special_separator|>
(170.52, 468.81) (176.56, 468.81) (176.56, 477.56) (170.52, 477.56)      /F128 x	<|special_separator|>
(176.57, 467.90) (179.58, 467.90) (179.58, 473.99) (176.57, 473.99)       /F26 t	<|special_separator|>
(179.57, 462.60) (185.80, 462.60) (185.80, 474.69) (179.57, 474.69)       /F29 -	<|special_separator|>
(185.80, 467.90) (189.77, 467.90) (189.77, 473.99) (185.80, 473.99)       /F23 1	<|special_separator|>
(190.27, 468.82) (202.47, 468.96) (202.47, 477.67) (190.27, 477.53)       /F24 ; ˜	<|special_separator|>
(194.70, 468.81) (201.75, 468.81) (201.75, 477.56) (194.70, 477.56)      /F131 µ	<|special_separator|>
(201.75, 466.96) (204.76, 466.96) (204.76, 473.05) (201.75, 473.05)       /F26 t	<|special_separator|>
(205.26, 468.82) (209.13, 468.82) (209.13, 477.53) (205.26, 477.53)       /F24 (	<|special_separator|>
(209.13, 468.81) (215.18, 468.81) (215.18, 477.56) (209.13, 477.56)      /F128 x	<|special_separator|>
(215.18, 467.90) (218.19, 467.90) (218.19, 473.99) (215.18, 473.99)       /F26 t	<|special_separator|>
(218.69, 468.82) (221.46, 468.82) (221.46, 477.53) (218.69, 477.53)       /F27 ,	<|special_separator|>
(223.12, 468.81) (229.16, 468.81) (229.16, 477.56) (223.12, 477.56)      /F128 x	<|special_separator|>
(229.16, 467.90) (233.13, 467.90) (233.13, 473.99) (229.16, 473.99)       /F23 0	<|special_separator|>
(233.63, 468.82) (237.51, 468.82) (237.51, 477.53) (233.63, 477.53)       /F24 )	<|special_separator|>
(237.51, 468.82) (240.27, 468.82) (240.27, 477.53) (237.51, 477.53)       /F27 ,	<|special_separator|>
(243.35, 471.45) (248.34, 471.45) (248.34, 480.16) (243.35, 480.16)       /F24 ˜	<|special_separator|>
(241.93, 468.82) (247.57, 468.82) (247.57, 477.53) (241.93, 477.53)       /F27 β	<|special_separator|>
(247.57, 467.90) (250.58, 467.90) (250.58, 473.99) (247.57, 473.99)       /F26 t	<|special_separator|>
(251.08, 468.81) (255.42, 468.81) (255.42, 477.56) (251.08, 477.56)      /F128 I	<|special_separator|>
(255.42, 468.82) (259.30, 468.82) (259.30, 477.53) (255.42, 477.53)       /F24 )	<|special_separator|>
(262.06, 468.82) (264.83, 468.82) (264.83, 477.53) (262.06, 477.53)       /F27 ,	<|special_separator|>
(288.40, 468.66) (300.02, 468.66) (300.02, 477.21) (288.40, 477.21)      /F123 (6)	<|special_separator|>
(048.96, 449.90) (073.30, 449.90) (073.30, 458.45) (048.96, 458.45)      /F123 where	<|special_separator|>
(074.19, 428.76) (079.17, 428.76) (079.17, 437.46) (074.19, 437.46)       /F24 ˜	<|special_separator|>
(073.16, 428.61) (080.21, 428.61) (080.21, 437.36) (073.16, 437.36)      /F131 µ	<|special_separator|>
(080.21, 426.75) (083.22, 426.75) (083.22, 432.85) (080.21, 432.85)       /F26 t	<|special_separator|>
(085.38, 428.62) (089.25, 428.62) (089.25, 437.33) (085.38, 437.33)       /F24 (	<|special_separator|>
(089.25, 428.61) (095.30, 428.61) (095.30, 437.36) (089.25, 437.36)      /F128 x	<|special_separator|>
(095.30, 427.70) (098.31, 427.70) (098.31, 433.79) (095.30, 433.79)       /F26 t	<|special_separator|>
(098.80, 428.62) (101.57, 428.62) (101.57, 437.33) (098.80, 437.33)       /F27 ,	<|special_separator|>
(103.23, 428.61) (109.28, 428.61) (109.28, 437.36) (103.23, 437.36)      /F128 x	<|special_separator|>
(109.28, 427.70) (113.25, 427.70) (113.25, 433.79) (109.28, 433.79)       /F23 0	<|special_separator|>
(113.75, 428.62) (128.14, 428.62) (128.14, 437.33) (113.75, 437.33)       /F24 ) =	<|special_separator|>
(132.10, 434.41) (140.40, 434.41) (140.40, 451.69) (132.10, 451.69)       /F30 √	<|special_separator|>
(141.40, 435.37) (146.38, 435.37) (146.38, 444.08) (141.40, 444.08)       /F24 ¯	<|special_separator|>
(140.40, 435.37) (146.78, 435.37) (146.78, 444.08) (140.40, 444.08)       /F27 α	<|special_separator|>
(146.78, 434.45) (149.79, 434.45) (149.79, 440.54) (146.78, 440.54)       /F26 t	<|special_separator|>
(149.79, 429.15) (156.01, 429.15) (156.01, 441.23) (149.79, 441.23)       /F29 -	<|special_separator|>
(156.01, 434.45) (159.99, 434.45) (159.99, 440.54) (156.01, 440.54)       /F23 1	<|special_separator|>
(160.48, 435.37) (166.12, 435.37) (166.12, 444.08) (160.48, 444.08)       /F27 β	<|special_separator|>
(166.12, 434.45) (169.13, 434.45) (169.13, 440.54) (166.12, 440.54)       /F26 t	<|special_separator|>
(137.34, 421.79) (142.32, 421.79) (142.32, 430.49) (137.34, 430.49)       /F24 1	<|special_separator|>
(144.54, 414.12) (152.29, 414.12) (152.29, 431.41) (144.54, 431.41)       /F30 -	<|special_separator|>
(155.49, 421.79) (160.47, 421.79) (160.47, 430.49) (155.49, 430.49)       /F24 ¯	<|special_separator|>
(154.50, 421.79) (160.88, 421.79) (160.88, 430.49) (154.50, 430.49)       /F27 α	<|special_separator|>
(160.88, 420.86) (163.88, 420.86) (163.88, 426.96) (160.88, 426.96)       /F26 t	<|special_separator|>
(170.82, 428.61) (176.87, 428.61) (176.87, 437.36) (170.82, 437.36)      /F128 x	<|special_separator|>
(176.87, 427.70) (180.84, 427.70) (180.84, 433.79) (176.87, 433.79)       /F23 0	<|special_separator|>
(183.55, 428.62) (191.30, 428.62) (191.30, 437.33) (183.55, 437.33)       /F24 +	<|special_separator|>
(194.71, 434.41) (203.01, 434.41) (203.01, 451.69) (194.71, 451.69)       /F30 √	<|special_separator|>
(203.01, 435.64) (209.38, 435.64) (209.38, 444.35) (203.01, 444.35)       /F27 α	<|special_separator|>
(209.38, 434.72) (212.39, 434.72) (212.39, 440.81) (209.38, 440.81)       /F26 t	<|special_separator|>
(214.55, 435.64) (223.41, 435.64) (223.41, 444.35) (214.55, 444.35)       /F24 (1	<|special_separator|>
(225.62, 427.98) (233.37, 427.98) (233.37, 445.26) (225.62, 445.26)       /F30 -	<|special_separator|>
(236.58, 435.64) (241.56, 435.64) (241.56, 444.35) (236.58, 444.35)       /F24 ¯	<|special_separator|>
(235.58, 435.64) (241.96, 435.64) (241.96, 444.35) (235.58, 444.35)       /F27 α	<|special_separator|>
(241.96, 434.72) (244.97, 434.72) (244.97, 440.81) (241.96, 440.81)       /F26 t	<|special_separator|>
(244.97, 429.42) (251.19, 429.42) (251.19, 441.50) (244.97, 441.50)       /F29 -	<|special_separator|>
(251.19, 434.72) (255.17, 434.72) (255.17, 440.81) (251.19, 440.81)       /F23 1	<|special_separator|>
(255.66, 435.64) (259.54, 435.64) (259.54, 444.35) (255.66, 444.35)       /F24 )	<|special_separator|>
(213.60, 421.79) (218.59, 421.79) (218.59, 430.49) (213.60, 430.49)       /F24 1	<|special_separator|>
(220.80, 414.12) (228.55, 414.12) (228.55, 431.41) (220.80, 431.41)       /F30 -	<|special_separator|>
(231.75, 421.79) (236.73, 421.79) (236.73, 430.49) (231.75, 430.49)       /F24 ¯	<|special_separator|>
(230.76, 421.79) (237.13, 421.79) (237.13, 430.49) (230.76, 430.49)       /F27 α	<|special_separator|>
(237.13, 420.86) (240.15, 420.86) (240.15, 426.96) (237.13, 426.96)       /F26 t	<|special_separator|>
(260.73, 428.61) (266.78, 428.61) (266.78, 437.36) (260.73, 437.36)      /F128 x	<|special_separator|>
(266.78, 427.70) (269.79, 427.70) (269.79, 433.79) (266.78, 433.79)       /F26 t	<|special_separator|>
(273.06, 428.62) (275.82, 428.62) (275.82, 437.33) (273.06, 437.33)       /F27 ,	<|special_separator|>
(288.40, 428.46) (300.02, 428.46) (300.02, 437.01) (288.40, 437.01)      /F123 (7)	<|special_separator|>
(048.96, 406.52) (063.35, 406.52) (063.35, 415.08) (048.96, 415.08)      /F123 and	<|special_separator|>
(142.52, 395.96) (147.50, 395.96) (147.50, 404.67) (142.52, 404.67)       /F24 ˜	<|special_separator|>
(141.10, 393.33) (146.74, 393.33) (146.74, 402.04) (141.10, 402.04)       /F27 β	<|special_separator|>
(146.74, 392.41) (149.75, 392.41) (149.75, 398.50) (146.74, 398.50)       /F26 t	<|special_separator|>
(153.01, 393.33) (160.76, 393.33) (160.76, 402.04) (153.01, 402.04)       /F24 =	<|special_separator|>
(164.73, 400.07) (169.71, 400.07) (169.71, 408.78) (164.73, 408.78)       /F24 1	<|special_separator|>
(171.92, 392.41) (179.67, 392.41) (179.67, 409.69) (171.92, 409.69)       /F30 -	<|special_separator|>
(182.88, 400.07) (187.86, 400.07) (187.86, 408.78) (182.88, 408.78)       /F24 ¯	<|special_separator|>
(181.88, 400.07) (188.26, 400.07) (188.26, 408.78) (181.88, 408.78)       /F27 α	<|special_separator|>
(188.26, 399.15) (191.27, 399.15) (191.27, 405.24) (188.26, 405.24)       /F26 t	<|special_separator|>
(191.27, 393.85) (197.49, 393.85) (197.49, 405.93) (191.27, 405.93)       /F29 -	<|special_separator|>
(197.49, 399.15) (201.47, 399.15) (201.47, 405.24) (197.49, 405.24)       /F23 1	<|special_separator|>
(169.82, 386.50) (174.81, 386.50) (174.81, 395.20) (169.82, 395.20)       /F24 1	<|special_separator|>
(177.02, 378.83) (184.77, 378.83) (184.77, 396.12) (177.02, 396.12)       /F30 -	<|special_separator|>
(187.97, 386.50) (192.96, 386.50) (192.96, 395.20) (187.97, 395.20)       /F24 ¯	<|special_separator|>
(186.98, 386.50) (193.36, 386.50) (193.36, 395.20) (186.98, 395.20)       /F27 α	<|special_separator|>
(193.36, 385.57) (196.37, 385.57) (196.37, 391.67) (193.36, 391.67)       /F26 t	<|special_separator|>
(203.16, 393.33) (208.79, 393.33) (208.79, 402.04) (203.16, 402.04)       /F27 β	<|special_separator|>
(208.79, 392.41) (211.80, 392.41) (211.80, 398.50) (208.79, 398.50)       /F26 t	<|special_separator|>
(215.07, 393.33) (217.84, 393.33) (217.84, 402.04) (215.07, 402.04)       /F27 .	<|special_separator|>
(288.40, 393.17) (300.02, 393.17) (300.02, 401.72) (288.40, 401.72)      /F123 (8)	<|special_separator|>
(048.96, 369.61) (092.28, 369.61) (092.28, 378.17) (048.96, 378.17)      /F123 because of	<|special_separator|>
(095.76, 369.77) (101.81, 369.77) (101.81, 378.51) (095.76, 378.51)      /F128 x	<|special_separator|>
(101.81, 368.85) (105.78, 368.85) (105.78, 374.95) (101.81, 374.95)       /F23 0	<|special_separator|>
(109.05, 369.78) (116.80, 369.78) (116.80, 378.48) (109.05, 378.48)       /F24 =	<|special_separator|>
(126.29, 374.27) (130.26, 374.27) (130.26, 380.37) (126.29, 380.37)       /F23 1	<|special_separator|>
(120.76, 366.26) (127.30, 366.26) (127.30, 378.35) (120.76, 378.35)       /F29 √	<|special_separator|>
(128.12, 366.53) (132.09, 366.53) (132.09, 372.62) (128.12, 372.62)       /F23 ¯	<|special_separator|>
(127.30, 366.53) (132.48, 366.53) (132.48, 372.62) (127.30, 372.62)       /F26 α	<|special_separator|>
(132.48, 365.91) (135.29, 365.91) (135.29, 370.27) (132.48, 370.27)       /F25 t	<|special_separator|>
(136.98, 369.78) (140.86, 369.78) (140.86, 378.48) (136.98, 378.48)       /F24 (	<|special_separator|>
(140.86, 369.77) (146.91, 369.77) (146.91, 378.51) (140.86, 378.51)      /F128 x	<|special_separator|>
(146.91, 368.85) (149.92, 368.85) (149.92, 374.95) (146.91, 374.95)       /F26 t	<|special_separator|>
(152.63, 362.12) (170.89, 369.61) (170.89, 386.89) (152.63, 379.40)       /F30 - √	<|special_separator|>
(170.89, 369.78) (175.87, 369.78) (175.87, 378.48) (170.89, 378.48)       /F24 1	<|special_separator|>
(178.09, 362.12) (185.84, 362.12) (185.84, 379.40) (178.09, 379.40)       /F30 -	<|special_separator|>
(189.04, 369.78) (194.02, 369.78) (194.02, 378.48) (189.04, 378.48)       /F24 ¯	<|special_separator|>
(188.05, 369.78) (194.42, 369.78) (194.42, 378.48) (188.05, 378.48)       /F27 α	<|special_separator|>
(194.42, 368.85) (197.43, 368.85) (197.43, 374.95) (194.42, 374.95)       /F26 t	<|special_separator|>
(197.93, 369.77) (202.75, 369.77) (202.75, 378.51) (197.93, 378.51)      /F131 ϵ	<|special_separator|>
(202.75, 368.85) (205.76, 368.85) (205.76, 374.95) (202.75, 374.95)       /F26 t	<|special_separator|>
(206.25, 369.78) (210.13, 369.78) (210.13, 378.48) (206.25, 378.48)       /F24 )	<|special_separator|>
(213.62, 369.61) (265.41, 369.61) (265.41, 378.17) (213.62, 378.17)      /F123 (Eq. 2), then	<|special_separator|>
(110.70, 344.53) (115.69, 344.53) (115.69, 353.23) (110.70, 353.23)       /F24 ˜	<|special_separator|>
(109.67, 344.38) (116.72, 344.38) (116.72, 353.13) (109.67, 353.13)      /F131 µ	<|special_separator|>
(116.72, 342.52) (119.73, 342.52) (119.73, 348.62) (116.72, 348.62)       /F26 t	<|special_separator|>
(123.00, 344.39) (130.75, 344.39) (130.75, 353.10) (123.00, 353.10)       /F24 =	<|special_separator|>
(141.31, 351.13) (146.29, 351.13) (146.29, 359.83) (141.31, 359.83)       /F24 1	<|special_separator|>
(134.71, 336.32) (143.01, 336.32) (143.01, 353.61) (134.71, 353.61)       /F30 √	<|special_separator|>
(143.01, 337.56) (149.38, 337.56) (149.38, 346.26) (143.01, 346.26)       /F27 α	<|special_separator|>
(149.38, 336.63) (152.39, 336.63) (152.39, 342.73) (149.38, 342.73)       /F26 t	<|special_separator|>
(154.09, 351.37) (160.04, 351.37) (160.04, 357.75) (154.09, 357.75)       /F17 (	<|special_separator|>
(160.04, 344.38) (166.08, 344.38) (166.08, 353.13) (160.04, 353.13)      /F128 x	<|special_separator|>
(166.08, 343.47) (169.09, 343.47) (169.09, 349.56) (166.08, 349.56)       /F26 t	<|special_separator|>
(171.81, 336.73) (179.55, 336.73) (179.55, 354.01) (171.81, 354.01)       /F30 -	<|special_separator|>
(187.12, 351.13) (192.10, 351.13) (192.10, 359.83) (187.12, 359.83)       /F24 1	<|special_separator|>
(194.31, 343.47) (202.06, 343.47) (202.06, 360.75) (194.31, 360.75)       /F30 -	<|special_separator|>
(204.27, 351.13) (210.65, 351.13) (210.65, 359.83) (204.27, 359.83)       /F27 α	<|special_separator|>
(210.65, 350.21) (213.66, 350.21) (213.66, 356.30) (210.65, 356.30)       /F26 t	<|special_separator|>
(182.96, 337.03) (191.27, 337.03) (191.27, 354.31) (182.96, 354.31)       /F30 √	<|special_separator|>
(191.27, 337.19) (196.25, 337.19) (196.25, 345.90) (191.27, 345.90)       /F24 1	<|special_separator|>
(198.46, 329.53) (206.21, 329.53) (206.21, 346.82) (198.46, 346.82)       /F30 -	<|special_separator|>
(209.41, 337.19) (214.40, 337.19) (214.40, 345.90) (209.41, 345.90)       /F24 ¯	<|special_separator|>
(208.42, 337.19) (214.80, 337.19) (214.80, 345.90) (208.42, 345.90)       /F27 α	<|special_separator|>
(214.80, 336.27) (217.81, 336.27) (217.81, 342.37) (214.80, 342.37)       /F26 t	<|special_separator|>
(219.50, 344.38) (224.31, 344.38) (224.31, 353.13) (219.50, 353.13)      /F131 ϵ	<|special_separator|>
(224.31, 343.47) (227.32, 343.47) (227.32, 349.56) (224.31, 349.56)       /F26 t	<|special_separator|>
(227.82, 351.37) (233.77, 351.37) (233.77, 357.75) (227.82, 357.75)       /F17 )	<|special_separator|>
(236.54, 344.39) (239.31, 344.39) (239.31, 353.10) (236.54, 353.10)       /F27 .	<|special_separator|>
(288.40, 344.23) (300.02, 344.23) (300.02, 352.78) (288.40, 352.78)      /F123 (9)	<|special_separator|>
(058.92, 320.79) (066.89, 320.79) (066.89, 329.08) (058.92, 329.08)      /F140 3)	<|special_separator|>
(071.38, 320.79) (105.09, 320.79) (105.09, 329.08) (071.38, 329.08)      /F140 Training:	<|special_separator|>
(111.69, 320.63) (125.38, 320.63) (125.38, 329.19) (111.69, 329.19)      /F123 For	<|special_separator|>
(131.50, 320.63) (143.67, 320.63) (143.67, 329.19) (131.50, 329.19)      /F123 the	<|special_separator|>
(149.78, 320.63) (178.14, 320.63) (178.14, 329.19) (149.78, 329.19)      /F123 reverse	<|special_separator|>
(184.26, 320.63) (219.99, 320.63) (219.99, 329.19) (184.26, 329.19)      /F123 diffusion	<|special_separator|>
(226.10, 320.63) (258.47, 320.63) (258.47, 329.19) (226.10, 329.19)      /F123 process,	<|special_separator|>
(264.59, 320.63) (269.01, 320.63) (269.01, 329.19) (264.59, 329.19)      /F123 a	<|special_separator|>
(275.12, 320.63) (300.02, 320.63) (300.02, 329.19) (275.12, 329.19)      /F123 neural	<|special_separator|>
(048.96, 308.68) (300.02, 308.68) (300.02, 317.23) (048.96, 317.23)      /F123 network is trained to approximate the conditional probability	<|special_separator|>
(048.96, 296.73) (101.07, 296.73) (101.07, 305.28) (048.96, 305.28)      /F123 distributions,	<|special_separator|>
(107.36, 296.73) (122.03, 296.73) (122.03, 305.28) (107.36, 305.28)      /F123 i.e.,	<|special_separator|>
(128.31, 296.73) (146.57, 296.73) (146.57, 305.28) (128.31, 305.28)      /F123 train	<|special_separator|>
(152.87, 296.88) (159.92, 296.88) (159.92, 305.62) (152.87, 305.62)      /F131 µ	<|special_separator|>
(159.92, 295.02) (163.71, 295.02) (163.71, 301.12) (159.92, 301.12)       /F26 θ	<|special_separator|>
(170.71, 296.73) (178.46, 296.73) (178.46, 305.28) (170.71, 305.28)      /F123 to	<|special_separator|>
(184.75, 296.73) (212.42, 296.73) (212.42, 305.28) (184.75, 305.28)      /F123 predict	<|special_separator|>
(219.74, 297.03) (224.72, 297.03) (224.72, 305.73) (219.74, 305.73)       /F24 ˜	<|special_separator|>
(218.71, 296.88) (225.76, 296.88) (225.76, 305.62) (218.71, 305.62)      /F131 µ	<|special_separator|>
(225.76, 295.02) (228.77, 295.02) (228.77, 301.12) (225.76, 301.12)       /F26 t	<|special_separator|>
(229.27, 296.73) (231.76, 296.73) (231.76, 305.28) (229.27, 305.28)      /F123 .	<|special_separator|>
(238.04, 296.73) (271.24, 296.73) (271.24, 305.28) (238.04, 305.28)      /F123 Because	<|special_separator|>
(277.53, 296.88) (283.58, 296.88) (283.58, 305.62) (277.53, 305.62)      /F128 x	<|special_separator|>
(283.58, 295.96) (286.59, 295.96) (286.59, 302.06) (283.58, 302.06)       /F26 t	<|special_separator|>
(293.37, 296.73) (300.02, 296.73) (300.02, 305.28) (293.37, 305.28)      /F123 is	<|special_separator|>
(048.96, 284.77) (084.48, 284.77) (084.48, 293.32) (048.96, 293.32)      /F123 available	<|special_separator|>
(088.82, 284.77) (105.70, 284.77) (105.70, 293.32) (088.82, 293.32)      /F123 (Eq.	<|special_separator|>
(110.05, 284.77) (118.35, 284.77) (118.35, 293.32) (110.05, 293.32)      /F123 9)	<|special_separator|>
(122.69, 284.77) (130.99, 284.77) (130.99, 293.32) (122.69, 293.32)      /F123 as	<|special_separator|>
(135.34, 284.77) (155.83, 284.77) (155.83, 293.32) (135.34, 293.32)      /F123 input	<|special_separator|>
(160.17, 284.77) (167.92, 284.77) (167.92, 293.32) (160.17, 293.32)      /F123 in	<|special_separator|>
(172.28, 284.77) (300.02, 284.77) (300.02, 293.32) (172.28, 293.32)      /F123 training time, it is common to	<|special_separator|>
(048.96, 272.81) (076.62, 272.81) (076.62, 281.37) (048.96, 281.37)      /F123 predict	<|special_separator|>
(080.11, 272.97) (084.93, 272.97) (084.93, 281.71) (080.11, 281.71)      /F131 ϵ	<|special_separator|>
(088.41, 272.81) (147.41, 272.81) (147.41, 281.37) (088.41, 281.37)      /F123 from the input	<|special_separator|>
(150.90, 272.97) (156.95, 272.97) (156.95, 281.71) (150.90, 281.71)      /F128 x	<|special_separator|>
(156.95, 272.06) (159.96, 272.06) (159.96, 278.15) (156.95, 278.15)       /F26 t	<|special_separator|>
(163.94, 272.81) (211.87, 272.81) (211.87, 281.37) (163.94, 281.37)      /F123 at time step	<|special_separator|>
(215.36, 272.98) (218.96, 272.98) (218.96, 281.68) (215.36, 281.68)       /F27 t	<|special_separator|>
(218.96, 272.81) (241.54, 272.81) (241.54, 281.37) (218.96, 281.37)      /F123 , thus	<|special_separator|>
(062.77, 250.99) (067.75, 250.99) (067.75, 259.70) (062.77, 259.70)       /F24 ˜	<|special_separator|>
(061.74, 250.84) (068.79, 250.84) (068.79, 259.59) (061.74, 259.59)      /F131 µ	<|special_separator|>
(068.79, 248.99) (071.80, 248.99) (071.80, 255.08) (068.79, 255.08)       /F26 t	<|special_separator|>
(075.06, 243.19) (082.81, 243.19) (082.81, 260.48) (075.06, 260.48)       /F30 ≈	<|special_separator|>
(085.58, 250.84) (092.63, 250.84) (092.63, 259.59) (085.58, 259.59)      /F131 µ	<|special_separator|>
(092.63, 248.99) (096.43, 248.99) (096.43, 255.08) (092.63, 255.08)       /F26 θ	<|special_separator|>
(097.14, 250.85) (101.01, 250.85) (101.01, 259.56) (097.14, 259.56)       /F24 (	<|special_separator|>
(101.02, 250.84) (107.06, 250.84) (107.06, 259.59) (101.02, 259.59)      /F128 x	<|special_separator|>
(107.06, 249.93) (110.07, 249.93) (110.07, 256.02) (107.06, 256.02)       /F26 t	<|special_separator|>
(110.57, 250.85) (118.60, 250.85) (118.60, 259.56) (110.57, 259.56)       /F27 , t	<|special_separator|>
(118.59, 250.85) (135.76, 250.85) (135.76, 259.56) (118.59, 259.56)       /F24 ) :=	<|special_separator|>
(146.32, 257.59) (151.30, 257.59) (151.30, 266.30) (146.32, 266.30)       /F24 1	<|special_separator|>
(139.72, 242.79) (148.02, 242.79) (148.02, 260.07) (139.72, 260.07)       /F30 √	<|special_separator|>
(148.02, 244.02) (154.39, 244.02) (154.39, 252.72) (148.02, 252.72)       /F27 α	<|special_separator|>
(154.39, 243.10) (157.40, 243.10) (157.40, 249.19) (154.39, 249.19)       /F26 t	<|special_separator|>
(159.09, 257.84) (165.04, 257.84) (165.04, 264.21) (159.09, 264.21)       /F17 (	<|special_separator|>
(165.04, 250.84) (171.09, 250.84) (171.09, 259.59) (165.04, 259.59)      /F128 x	<|special_separator|>
(171.09, 249.93) (174.10, 249.93) (174.10, 256.02) (171.09, 256.02)       /F26 t	<|special_separator|>
(176.81, 243.19) (184.56, 243.19) (184.56, 260.48) (176.81, 260.48)       /F30 -	<|special_separator|>
(192.12, 257.59) (197.10, 257.59) (197.10, 266.30) (192.12, 266.30)       /F24 1	<|special_separator|>
(199.32, 249.93) (207.06, 249.93) (207.06, 267.22) (199.32, 267.22)       /F30 -	<|special_separator|>
(209.28, 257.59) (215.65, 257.59) (215.65, 266.30) (209.28, 266.30)       /F27 α	<|special_separator|>
(215.65, 256.67) (218.66, 256.67) (218.66, 262.76) (215.65, 262.76)       /F26 t	<|special_separator|>
(187.97, 243.49) (196.27, 243.49) (196.27, 260.77) (187.97, 260.77)       /F30 √	<|special_separator|>
(196.27, 243.66) (201.25, 243.66) (201.25, 252.36) (196.27, 252.36)       /F24 1	<|special_separator|>
(203.47, 236.00) (211.22, 236.00) (211.22, 253.28) (203.47, 253.28)       /F30 -	<|special_separator|>
(214.42, 243.66) (219.40, 243.66) (219.40, 252.36) (214.42, 252.36)       /F24 ¯	<|special_separator|>
(213.43, 243.66) (219.80, 243.66) (219.80, 252.36) (213.43, 252.36)       /F27 α	<|special_separator|>
(219.80, 242.74) (222.81, 242.74) (222.81, 248.83) (219.80, 248.83)       /F26 t	<|special_separator|>
(224.42, 250.99) (229.40, 250.99) (229.40, 259.70) (224.42, 259.70)       /F24 ˜	<|special_separator|>
(224.51, 250.84) (229.32, 250.84) (229.32, 259.59) (224.51, 259.59)      /F131 ϵ	<|special_separator|>
(229.32, 249.93) (233.12, 249.93) (233.12, 256.02) (229.32, 256.02)       /F26 θ	<|special_separator|>
(233.83, 250.85) (237.70, 250.85) (237.70, 259.56) (233.83, 259.56)       /F24 (	<|special_separator|>
(237.70, 250.84) (243.75, 250.84) (243.75, 259.59) (237.70, 259.59)      /F128 x	<|special_separator|>
(243.75, 249.93) (246.76, 249.93) (246.76, 256.02) (243.75, 256.02)       /F26 t	<|special_separator|>
(247.26, 250.85) (255.29, 250.85) (255.29, 259.56) (247.26, 259.56)       /F27 , t	<|special_separator|>
(255.28, 250.85) (259.16, 250.85) (259.16, 259.56) (255.28, 259.56)       /F24 )	<|special_separator|>
(259.16, 257.84) (265.11, 257.84) (265.11, 264.21) (259.16, 264.21)       /F17 )	<|special_separator|>
(267.88, 250.85) (270.64, 250.85) (270.64, 259.56) (267.88, 259.56)       /F27 .	<|special_separator|>
(283.42, 250.69) (300.02, 250.69) (300.02, 259.24) (283.42, 259.24)      /F123 (10)	<|special_separator|>
(048.96, 224.63) (089.67, 224.63) (089.67, 233.18) (048.96, 233.18)      /F123 By letting	<|special_separator|>
(093.28, 224.78) (101.55, 224.78) (101.55, 233.53) (093.28, 233.53)      /F128 Σ	<|special_separator|>
(101.55, 223.87) (105.35, 223.87) (105.35, 229.96) (101.55, 229.96)       /F26 θ	<|special_separator|>
(106.06, 224.79) (109.93, 224.79) (109.93, 233.50) (106.06, 233.50)       /F24 (	<|special_separator|>
(109.93, 224.78) (115.98, 224.78) (115.98, 233.53) (109.93, 233.53)      /F128 x	<|special_separator|>
(115.98, 223.87) (118.99, 223.87) (118.99, 229.96) (115.98, 229.96)       /F26 t	<|special_separator|>
(119.49, 224.79) (127.52, 224.79) (127.52, 233.50) (119.49, 233.50)       /F27 , t	<|special_separator|>
(127.51, 224.79) (142.14, 224.79) (142.14, 233.50) (127.51, 233.50)       /F24 ) =	<|special_separator|>
(146.56, 227.42) (151.54, 227.42) (151.54, 236.13) (146.56, 236.13)       /F24 ˜	<|special_separator|>
(145.14, 224.79) (150.78, 224.79) (150.78, 233.50) (145.14, 233.50)       /F27 β	<|special_separator|>
(150.78, 223.87) (153.79, 223.87) (153.79, 229.96) (150.78, 229.96)       /F26 t	<|special_separator|>
(154.29, 224.78) (158.63, 224.78) (158.63, 233.53) (154.29, 233.53)      /F128 I	<|special_separator|>
(158.63, 224.63) (300.02, 224.63) (300.02, 233.18) (158.63, 233.18)      /F123 , and letting the forward variances	<|special_separator|>
(048.96, 212.84) (054.59, 212.84) (054.59, 221.54) (048.96, 221.54)       /F27 β	<|special_separator|>
(054.59, 211.91) (057.60, 211.91) (057.60, 218.01) (054.59, 218.01)       /F26 t	<|special_separator|>
(060.81, 212.67) (276.69, 212.67) (276.69, 221.23) (060.81, 221.23)      /F123 to be a sequence of linearly increasing constants from	<|special_separator|>
(279.40, 212.84) (285.03, 212.84) (285.03, 221.54) (279.40, 221.54)       /F27 β	<|special_separator|>
(285.03, 211.91) (289.00, 211.91) (289.00, 218.01) (285.03, 218.01)       /F23 1	<|special_separator|>
(292.27, 212.84) (300.02, 212.84) (300.02, 221.54) (292.27, 221.54)       /F24 =	<|special_separator|>
(048.96, 200.88) (058.92, 200.88) (058.92, 209.59) (048.96, 209.59)       /F24 10	<|special_separator|>
(058.92, 199.77) (065.15, 199.77) (065.15, 211.85) (058.92, 211.85)       /F29 -	<|special_separator|>
(065.15, 205.07) (069.12, 205.07) (069.12, 211.16) (065.15, 211.16)       /F23 4	<|special_separator|>
(074.38, 200.72) (082.13, 200.72) (082.13, 209.27) (074.38, 209.27)      /F123 to	<|special_separator|>
(086.88, 200.88) (092.52, 200.88) (092.52, 209.59) (086.88, 209.59)       /F27 β	<|special_separator|>
(092.52, 199.96) (097.22, 199.96) (097.22, 206.05) (092.52, 206.05)       /F26 T	<|special_separator|>
(103.91, 200.88) (121.76, 200.88) (121.76, 209.59) (103.91, 209.59)       /F24 = 0	<|special_separator|>
(121.76, 200.88) (124.53, 200.88) (124.53, 209.59) (121.76, 209.59)       /F27 .	<|special_separator|>
(124.53, 200.88) (134.49, 200.88) (134.49, 209.59) (124.53, 209.59)       /F24 02	<|special_separator|>
(134.49, 200.72) (136.98, 200.72) (136.98, 209.27) (134.49, 209.27)      /F123 ,	<|special_separator|>
(141.74, 200.72) (207.14, 200.72) (207.14, 209.27) (141.74, 209.27)      /F123 and some other	<|special_separator|>
(211.90, 200.72) (270.58, 200.72) (270.58, 209.27) (211.90, 209.27)      /F123 simplifications	<|special_separator|>
(275.33, 200.72) (283.08, 200.72) (283.08, 209.27) (275.33, 209.27)      /F123 in	<|special_separator|>
(287.85, 200.72) (300.02, 200.72) (300.02, 209.27) (287.85, 209.27)      /F123 the	<|special_separator|>
(048.96, 188.76) (093.06, 188.76) (093.06, 197.32) (048.96, 197.32)      /F123 work [26],	<|special_separator|>
(097.72, 188.76) (287.62, 188.76) (287.62, 197.32) (097.72, 197.32)      /F123 we can minimize the MSE loss of the noise	<|special_separator|>
(292.27, 188.76) (300.02, 188.76) (300.02, 197.32) (292.27, 197.32)      /F123 to	<|special_separator|>
(048.96, 176.81) (149.79, 176.81) (149.79, 185.36) (048.96, 185.36)      /F123 train the neural network.	<|special_separator|>
(108.88, 160.11) (115.52, 160.11) (115.52, 164.73) (108.88, 164.73)      /F110 E	<|special_separator|>
(115.52, 156.98) (118.53, 156.98) (118.53, 163.07) (115.52, 163.07)       /F26 t	<|special_separator|>
(118.53, 151.68) (124.76, 151.68) (124.76, 163.77) (118.53, 163.77)       /F29 ∼	<|special_separator|>
(124.76, 156.98) (130.98, 156.98) (130.98, 163.07) (124.76, 163.07)       /F23 [1	<|special_separator|>
(130.98, 156.98) (138.05, 156.98) (138.05, 163.07) (130.98, 163.07)       /F26 ,T	<|special_separator|>
(139.13, 156.98) (141.38, 156.98) (141.38, 163.07) (139.13, 163.07)       /F23 ]	<|special_separator|>
(141.38, 156.98) (143.75, 156.98) (143.75, 163.07) (141.38, 163.07)       /F26 ,	<|special_separator|>
(143.75, 156.97) (148.51, 156.97) (148.51, 163.10) (143.75, 163.10)      /F129 x	<|special_separator|>
(148.51, 156.37) (151.90, 156.37) (151.90, 160.70) (148.51, 160.70)       /F22 0	<|special_separator|>
(152.40, 156.98) (154.76, 156.98) (154.76, 163.07) (152.40, 163.07)       /F26 ,	<|special_separator|>
(154.76, 156.97) (158.58, 156.97) (158.58, 163.10) (154.76, 163.10)      /F132 ϵ	<|special_separator|>
(159.08, 165.19) (163.78, 165.19) (163.78, 171.57) (159.08, 171.57)       /F17 [	<|special_separator|>
(163.78, 150.55) (168.77, 150.55) (168.77, 167.83) (163.78, 167.83)       /F30 ∥	<|special_separator|>
(168.77, 158.20) (173.58, 158.20) (173.58, 166.94) (168.77, 166.94)      /F131 ϵ	<|special_separator|>
(175.80, 150.55) (183.54, 150.55) (183.54, 167.83) (175.80, 167.83)       /F30 -	<|special_separator|>
(185.68, 158.35) (190.66, 158.35) (190.66, 167.05) (185.68, 167.05)       /F24 ˜	<|special_separator|>
(185.76, 158.20) (190.57, 158.20) (190.57, 166.94) (185.76, 166.94)      /F131 ϵ	<|special_separator|>
(190.57, 157.29) (194.37, 157.29) (194.37, 163.38) (190.57, 163.38)       /F26 θ	<|special_separator|>
(195.08, 158.21) (198.96, 158.21) (198.96, 166.91) (195.08, 166.91)       /F24 (	<|special_separator|>
(198.96, 158.20) (205.00, 158.20) (205.00, 166.94) (198.96, 166.94)      /F128 x	<|special_separator|>
(205.00, 157.29) (208.01, 157.29) (208.01, 163.38) (205.00, 163.38)       /F26 t	<|special_separator|>
(208.51, 158.21) (216.54, 158.21) (216.54, 166.91) (208.51, 166.91)       /F27 , t	<|special_separator|>
(216.53, 158.21) (220.41, 158.21) (220.41, 166.91) (216.53, 166.91)       /F24 )	<|special_separator|>
(220.41, 150.55) (225.39, 150.55) (225.39, 167.83) (220.41, 167.83)       /F30 ∥	<|special_separator|>
(225.39, 162.89) (229.36, 162.89) (229.36, 168.99) (225.39, 168.99)       /F23 2	<|special_separator|>
(229.86, 165.19) (234.56, 165.19) (234.56, 171.57) (229.86, 171.57)       /F17 ]	<|special_separator|>
(237.33, 158.21) (240.10, 158.21) (240.10, 166.91) (237.33, 166.91)       /F27 .	<|special_separator|>
(283.42, 158.04) (300.02, 158.04) (300.02, 166.60) (283.42, 166.60)      /F123 (11)	<|special_separator|>
(058.92, 138.10) (066.89, 138.10) (066.89, 146.40) (058.92, 146.40)      /F140 4)	<|special_separator|>
(071.38, 138.10) (110.98, 138.10) (110.98, 146.40) (071.38, 146.40)      /F140 Inference:	<|special_separator|>
(115.67, 137.95) (300.02, 137.95) (300.02, 146.50) (115.67, 146.50)      /F123 A neural network trained in the reverse dif-	<|special_separator|>
(048.96, 125.99) (300.02, 125.99) (300.02, 134.54) (048.96, 134.54)      /F123 fusion process can be used to generate data. This is achieved	<|special_separator|>
(048.96, 114.04) (106.19, 114.04) (106.19, 122.59) (048.96, 122.59)      /F123 by initializing	<|special_separator|>
(110.28, 114.19) (116.33, 114.19) (116.33, 122.94) (110.28, 122.94)      /F128 x	<|special_separator|>
(116.33, 113.28) (121.04, 113.28) (121.04, 119.37) (116.33, 119.37)       /F26 T	<|special_separator|>
(126.50, 106.54) (146.31, 106.54) (146.31, 123.83) (126.50, 123.83)       /F30 ∼ N	<|special_separator|>
(147.78, 114.20) (151.65, 114.20) (151.65, 122.91) (147.78, 122.91)       /F24 (	<|special_separator|>
(151.65, 114.19) (157.38, 114.19) (157.38, 122.94) (151.65, 122.94)      /F128 0	<|special_separator|>
(157.38, 114.20) (160.15, 114.20) (160.15, 122.91) (157.38, 122.91)       /F27 ,	<|special_separator|>
(161.81, 114.19) (167.54, 114.19) (167.54, 122.94) (161.81, 122.94)      /F128 1	<|special_separator|>
(167.54, 114.20) (171.41, 114.20) (171.41, 122.91) (167.54, 122.91)       /F24 )	<|special_separator|>
(175.50, 114.04) (300.02, 114.04) (300.02, 122.59) (175.50, 122.59)      /F123 and, in T steps, denoising the	<|special_separator|>
(048.96, 102.08) (111.83, 102.08) (111.83, 110.63) (048.96, 110.63)      /F123 image by using	<|special_separator|>
(061.95, 078.83) (068.00, 078.83) (068.00, 087.57) (061.95, 087.57)      /F128 x	<|special_separator|>
(068.00, 077.91) (071.01, 077.91) (071.01, 084.01) (068.00, 084.01)       /F26 t	<|special_separator|>
(071.01, 072.61) (077.23, 072.61) (077.23, 084.70) (071.01, 084.70)       /F29 -	<|special_separator|>
(077.23, 077.91) (081.21, 077.91) (081.21, 084.01) (077.23, 084.01)       /F23 1	<|special_separator|>
(084.47, 078.84) (092.22, 078.84) (092.22, 087.54) (084.47, 087.54)       /F24 =	<|special_separator|>
(102.78, 085.58) (107.76, 085.58) (107.76, 094.28) (102.78, 094.28)       /F24 1	<|special_separator|>
(096.18, 070.77) (104.48, 070.77) (104.48, 088.05) (096.18, 088.05)       /F30 √	<|special_separator|>
(104.48, 072.00) (110.86, 072.00) (110.86, 080.71) (104.48, 080.71)       /F27 α	<|special_separator|>
(110.86, 071.08) (113.87, 071.08) (113.87, 077.17) (110.86, 077.17)       /F26 t	<|special_separator|>
(117.22, 088.81) (124.55, 088.81) (124.55, 095.18) (117.22, 095.18)       /F17 (	<|special_separator|>
(124.55, 078.83) (130.60, 078.83) (130.60, 087.57) (124.55, 087.57)      /F128 x	<|special_separator|>
(130.60, 077.91) (133.61, 077.91) (133.61, 084.01) (130.60, 084.01)       /F26 t	<|special_separator|>
(136.32, 071.17) (144.07, 071.17) (144.07, 088.46) (136.32, 088.46)       /F30 -	<|special_separator|>
(151.63, 085.58) (156.61, 085.58) (156.61, 094.28) (151.63, 094.28)       /F24 1	<|special_separator|>
(158.83, 077.91) (166.58, 077.91) (166.58, 095.20) (158.83, 095.20)       /F30 -	<|special_separator|>
(168.79, 085.58) (175.16, 085.58) (175.16, 094.28) (168.79, 094.28)       /F27 α	<|special_separator|>
(175.16, 084.65) (178.17, 084.65) (178.17, 090.75) (175.16, 090.75)       /F26 t	<|special_separator|>
(147.48, 071.47) (155.78, 071.47) (155.78, 088.76) (147.48, 088.76)       /F30 √	<|special_separator|>
(155.78, 071.64) (160.76, 071.64) (160.76, 080.35) (155.78, 080.35)       /F24 1	<|special_separator|>
(162.98, 063.98) (170.73, 063.98) (170.73, 081.26) (162.98, 081.26)       /F30 -	<|special_separator|>
(173.93, 071.64) (178.91, 071.64) (178.91, 080.35) (173.93, 080.35)       /F24 ¯	<|special_separator|>
(172.94, 071.64) (179.31, 071.64) (179.31, 080.35) (172.94, 080.35)       /F27 α	<|special_separator|>
(179.31, 070.72) (182.32, 070.72) (182.32, 076.81) (179.31, 076.81)       /F26 t	<|special_separator|>
(183.93, 078.97) (188.91, 078.97) (188.91, 087.68) (183.93, 087.68)       /F24 ˜	<|special_separator|>
(184.02, 078.83) (188.83, 078.83) (188.83, 087.57) (184.02, 087.57)      /F131 ϵ	<|special_separator|>
(188.83, 077.91) (192.63, 077.91) (192.63, 084.01) (188.83, 084.01)       /F26 θ	<|special_separator|>
(195.00, 078.84) (198.87, 078.84) (198.87, 087.54) (195.00, 087.54)       /F24 (	<|special_separator|>
(198.88, 078.83) (204.92, 078.83) (204.92, 087.57) (198.88, 087.57)      /F128 x	<|special_separator|>
(204.92, 077.91) (207.93, 077.91) (207.93, 084.01) (204.92, 084.01)       /F26 t	<|special_separator|>
(208.43, 078.84) (216.46, 078.84) (216.46, 087.54) (208.43, 087.54)       /F27 , t	<|special_separator|>
(216.46, 078.84) (220.33, 078.84) (220.33, 087.54) (216.46, 087.54)       /F24 )	<|special_separator|>
(220.33, 088.81) (227.66, 088.81) (227.66, 095.18) (220.33, 095.18)       /F17 )	<|special_separator|>
(229.88, 078.84) (237.62, 078.84) (237.62, 087.54) (229.88, 087.54)       /F24 +	<|special_separator|>
(239.84, 087.94) (249.80, 087.94) (249.80, 094.31) (239.84, 094.31)       /F17 √	<|special_separator|>
(251.22, 081.47) (256.20, 081.47) (256.20, 090.17) (251.22, 090.17)       /F24 ˜	<|special_separator|>
(249.80, 078.84) (255.44, 078.84) (255.44, 087.54) (249.80, 087.54)       /F27 β	<|special_separator|>
(255.44, 077.91) (258.45, 077.91) (258.45, 084.01) (255.44, 084.01)       /F26 t	<|special_separator|>
(258.94, 078.83) (264.48, 078.83) (264.48, 087.57) (258.94, 087.57)      /F131 z	<|special_separator|>
(267.66, 078.84) (270.43, 078.84) (270.43, 087.54) (267.66, 087.54)       /F27 .	<|special_separator|>
(283.42, 078.67) (300.02, 078.67) (300.02, 087.22) (283.42, 087.22)      /F123 (12)	<|special_separator|>
(048.96, 054.42) (073.30, 054.42) (073.30, 062.97) (048.96, 062.97)      /F123 where	<|special_separator|>
(076.61, 054.58) (081.70, 054.58) (081.70, 063.32) (076.61, 063.32)      /F128 z	<|special_separator|>
(084.47, 046.92) (103.16, 046.92) (103.16, 064.21) (084.47, 064.21)       /F30 ∼ N	<|special_separator|>
(104.62, 054.59) (108.50, 054.59) (108.50, 063.29) (104.62, 063.29)       /F24 (	<|special_separator|>
(108.50, 054.58) (114.23, 054.58) (114.23, 063.32) (108.50, 063.32)      /F128 0	<|special_separator|>
(114.23, 054.59) (117.00, 054.59) (117.00, 063.29) (114.23, 063.29)       /F27 ,	<|special_separator|>
(118.66, 054.58) (124.38, 054.58) (124.38, 063.32) (118.66, 063.32)      /F128 1	<|special_separator|>
(124.39, 054.59) (128.26, 054.59) (128.26, 063.29) (124.39, 063.29)       /F24 )	<|special_separator|>
(131.57, 054.42) (300.02, 054.42) (300.02, 062.97) (131.57, 062.97)      /F123 is new noise added between each denois-	<|special_separator|>
(048.96, 042.47) (083.72, 042.47) (083.72, 051.02) (048.96, 051.02)      /F123 ing step.	<|special_separator|>
(406.25, 498.61) (468.77, 499.17) (468.77, 509.04) (406.25, 510.94)      /F115 III. METHODS	<|special_separator|>
(321.94, 482.85) (500.09, 482.85) (500.09, 491.40) (321.94, 491.40)      /F123 The classical DDPM approach requires only	<|special_separator|>
(502.85, 483.00) (508.90, 483.00) (508.90, 491.75) (502.85, 491.75)      /F128 x	<|special_separator|>
(508.90, 482.09) (511.91, 482.09) (511.91, 488.18) (508.90, 488.18)       /F26 t	<|special_separator|>
(515.17, 482.85) (563.03, 482.85) (563.03, 491.40) (515.17, 491.40)      /F123 for training,	<|special_separator|>
(311.97, 470.89) (427.42, 470.89) (427.42, 479.44) (311.97, 479.44)      /F123 resulting in arbitrary images	<|special_separator|>
(430.86, 471.05) (436.90, 471.05) (436.90, 479.79) (430.86, 479.79)      /F128 x	<|special_separator|>
(436.91, 470.13) (440.88, 470.13) (440.88, 476.23) (436.91, 476.23)       /F23 0	<|special_separator|>
(444.81, 470.89) (563.03, 470.89) (563.03, 479.44) (444.81, 479.44)      /F123 when sampling from random	<|special_separator|>
(311.97, 458.94) (563.03, 458.94) (563.03, 467.49) (311.97, 467.49)      /F123 noise during inference. However, our goal is not to generate	<|special_separator|>
(311.97, 446.98) (346.27, 446.98) (346.27, 455.53) (311.97, 455.53)      /F123 arbitrary	<|special_separator|>
(351.53, 446.98) (379.76, 446.98) (379.76, 455.53) (351.53, 455.53)      /F123 images	<|special_separator|>
(385.02, 446.98) (397.55, 446.98) (397.55, 455.53) (385.02, 455.53)      /F123 but	<|special_separator|>
(402.81, 446.98) (410.56, 446.98) (410.56, 455.53) (402.81, 455.53)      /F123 to	<|special_separator|>
(415.82, 446.98) (449.57, 446.98) (449.57, 455.53) (415.82, 455.53)      /F123 generate	<|special_separator|>
(454.83, 446.98) (486.37, 446.98) (486.37, 455.53) (454.83, 455.53)      /F123 realistic	<|special_separator|>
(491.63, 446.98) (563.03, 446.98) (563.03, 455.53) (491.63, 455.53)      /F123 MRIs and tumor	<|special_separator|>
(311.97, 435.02) (563.03, 435.02) (563.03, 443.58) (311.97, 443.58)      /F123 growth maps for any target (future) treatment-day point from	<|special_separator|>
(311.97, 423.07) (563.03, 423.07) (563.03, 431.62) (311.97, 431.62)      /F123 a given sequence of source/conditioning images and treatment	<|special_separator|>
(311.97, 411.11) (361.51, 411.11) (361.51, 419.67) (311.97, 419.67)      /F123 information.	<|special_separator|>
(367.25, 411.11) (377.52, 411.11) (377.52, 419.67) (367.25, 419.67)      /F123 To	<|special_separator|>
(383.25, 411.11) (397.65, 411.11) (397.65, 419.67) (383.25, 419.67)      /F123 this	<|special_separator|>
(403.39, 411.11) (420.27, 411.11) (420.27, 419.67) (403.39, 419.67)      /F123 end,	<|special_separator|>
(426.00, 411.11) (474.90, 411.11) (474.90, 419.67) (426.00, 419.67)      /F123 we propose	<|special_separator|>
(480.64, 411.11) (492.81, 411.11) (492.81, 419.67) (480.64, 419.67)      /F123 the	<|special_separator|>
(498.55, 411.11) (563.03, 411.11) (563.03, 419.67) (498.55, 419.67)      /F123 treatment-aware	<|special_separator|>
(311.97, 399.16) (563.03, 399.16) (563.03, 407.71) (311.97, 407.71)      /F123 diffusion (TaDiff) model for multi-parametric MRI generation	<|special_separator|>
(311.97, 387.20) (563.03, 387.20) (563.03, 395.76) (311.97, 395.76)      /F123 and tumor growth prediction on longitudinal data. Our TaDiff	<|special_separator|>
(311.97, 375.25) (563.03, 375.25) (563.03, 383.80) (311.97, 383.80)      /F123 model introduces a treatment-aware mechanism for condition-	<|special_separator|>
(311.97, 363.29) (563.03, 363.29) (563.03, 371.85) (311.97, 371.85)      /F123 ing a diffusion model while also employing a joint learning	<|special_separator|>
(311.97, 351.34) (343.37, 351.34) (343.37, 359.89) (311.97, 359.89)      /F123 strategy	<|special_separator|>
(347.77, 351.34) (355.52, 351.34) (355.52, 359.89) (347.77, 359.89)      /F123 to	<|special_separator|>
(359.92, 351.34) (502.46, 351.34) (502.46, 359.89) (359.92, 359.89)      /F123 segment the tumor and project its	<|special_separator|>
(506.86, 351.34) (563.03, 351.34) (563.03, 359.89) (506.86, 359.89)      /F123 future growth	<|special_separator|>
(311.97, 339.38) (563.03, 339.38) (563.03, 347.94) (311.97, 347.94)      /F123 during diffusion processes. Figure 2 illustrates an overview of	<|special_separator|>
(311.97, 327.43) (391.77, 327.43) (391.77, 335.98) (311.97, 335.98)      /F123 the TaDiff pipeline.	<|special_separator|>
(311.97, 297.69) (321.39, 297.69) (321.39, 306.90) (311.97, 306.90)      /F140 A.	<|special_separator|>
(326.37, 297.69) (402.02, 297.69) (402.02, 306.90) (326.37, 306.90)      /F140 Problem Settings	<|special_separator|>
(321.94, 281.81) (418.80, 281.81) (418.80, 290.36) (321.94, 290.36)      /F123 Let tumor binary masks	<|special_separator|>
(421.94, 281.97) (432.82, 281.97) (432.82, 290.71) (421.94, 290.71)      /F128 M	<|special_separator|>
(435.59, 274.31) (442.23, 274.31) (442.23, 291.60) (435.59, 291.60)       /F30 ∈	<|special_separator|>
(445.00, 283.88) (452.19, 283.88) (452.19, 288.50) (445.00, 288.50)      /F110 R	<|special_separator|>
(452.19, 286.16) (457.65, 286.16) (457.65, 292.25) (452.19, 292.25)       /F26 L	<|special_separator|>
(457.66, 280.86) (463.88, 280.86) (463.88, 292.95) (457.66, 292.95)       /F29 ×	<|special_separator|>
(463.88, 286.16) (470.41, 286.16) (470.41, 292.25) (463.88, 292.25)       /F26 H	<|special_separator|>
(470.94, 280.86) (477.17, 280.86) (477.17, 292.95) (470.94, 292.95)       /F29 ×	<|special_separator|>
(477.17, 286.16) (484.66, 286.16) (484.66, 292.25) (477.17, 292.25)       /F26 W	<|special_separator|>
(485.73, 280.86) (491.96, 280.86) (491.96, 292.95) (485.73, 292.95)       /F29 ×	<|special_separator|>
(491.96, 286.16) (498.47, 286.16) (498.47, 292.25) (491.96, 292.25)       /F26 D	<|special_separator|>
(502.33, 281.81) (563.03, 281.81) (563.03, 290.36) (502.33, 290.36)      /F123 be longitudinal	<|special_separator|>
(311.97, 269.86) (479.01, 269.86) (479.01, 278.41) (311.97, 278.41)      /F123 3D tumor volumes with temporal length	<|special_separator|>
(482.90, 270.02) (489.68, 270.02) (489.68, 278.73) (482.90, 278.73)       /F27 L	<|special_separator|>
(489.68, 269.86) (563.03, 269.86) (563.03, 278.41) (489.68, 278.41)      /F123 . The correspond-	<|special_separator|>
(311.97, 257.90) (324.70, 257.90) (324.70, 266.45) (311.97, 266.45)      /F123 ing	<|special_separator|>
(329.83, 257.90) (377.99, 257.90) (377.99, 266.45) (329.83, 266.45)      /F123 longitudinal	<|special_separator|>
(383.11, 257.90) (428.62, 257.90) (428.62, 266.45) (383.11, 266.45)      /F123 MRI scans	<|special_separator|>
(433.74, 258.06) (442.40, 258.06) (442.40, 266.80) (433.74, 266.80)      /F128 X	<|special_separator|>
(448.19, 250.40) (454.83, 250.40) (454.83, 267.69) (448.19, 267.69)       /F30 ∈	<|special_separator|>
(460.62, 259.97) (467.82, 259.97) (467.82, 264.59) (460.62, 264.59)      /F110 R	<|special_separator|>
(467.82, 262.25) (473.29, 262.25) (473.29, 268.34) (467.82, 268.34)       /F26 L	<|special_separator|>
(473.29, 256.95) (479.51, 256.95) (479.51, 269.04) (473.29, 269.04)       /F29 ×	<|special_separator|>
(479.51, 262.25) (485.23, 262.25) (485.23, 268.34) (479.51, 268.34)       /F26 C	<|special_separator|>
(485.72, 256.95) (491.94, 256.95) (491.94, 269.04) (485.72, 269.04)       /F29 ×	<|special_separator|>
(491.94, 262.25) (498.47, 262.25) (498.47, 268.34) (491.94, 268.34)       /F26 H	<|special_separator|>
(499.00, 256.95) (505.23, 256.95) (505.23, 269.04) (499.00, 269.04)       /F29 ×	<|special_separator|>
(505.23, 262.25) (512.72, 262.25) (512.72, 268.34) (505.23, 268.34)       /F26 W	<|special_separator|>
(513.79, 256.95) (520.02, 256.95) (520.02, 269.04) (513.79, 269.04)       /F29 ×	<|special_separator|>
(520.02, 262.25) (526.53, 262.25) (526.53, 268.34) (520.02, 268.34)       /F26 D	<|special_separator|>
(532.37, 257.90) (550.08, 257.90) (550.08, 266.45) (532.37, 266.45)      /F123 with	<|special_separator|>
(555.20, 258.06) (562.32, 258.06) (562.32, 266.77) (555.20, 266.77)       /F27 C	<|special_separator|>
(311.97, 245.94) (349.32, 245.94) (349.32, 254.50) (311.97, 254.50)      /F123 channels.	<|special_separator|>
(354.38, 245.94) (362.68, 245.94) (362.68, 254.50) (354.38, 254.50)      /F123 In	<|special_separator|>
(367.74, 245.94) (379.92, 245.94) (379.92, 254.50) (367.74, 254.50)      /F123 the	<|special_separator|>
(384.97, 245.94) (413.18, 245.94) (413.18, 254.50) (384.97, 254.50)      /F123 current	<|special_separator|>
(418.24, 245.94) (441.68, 245.94) (441.68, 254.50) (418.24, 254.50)      /F123 study,	<|special_separator|>
(446.74, 245.94) (497.17, 245.94) (497.17, 254.50) (446.74, 254.50)      /F123 we consider	<|special_separator|>
(502.23, 246.11) (509.35, 246.11) (509.35, 254.81) (502.23, 254.81)       /F27 C	<|special_separator|>
(515.12, 245.94) (550.23, 245.94) (550.23, 254.50) (515.12, 254.50)      /F123 = 3 due	<|special_separator|>
(555.28, 245.94) (563.03, 245.94) (563.03, 254.50) (555.28, 254.50)      /F123 to	<|special_separator|>
(311.97, 233.99) (324.15, 233.99) (324.15, 242.54) (311.97, 242.54)      /F123 the	<|special_separator|>
(328.89, 233.99) (373.27, 233.99) (373.27, 242.54) (328.89, 242.54)      /F123 availability	<|special_separator|>
(378.01, 233.99) (386.31, 233.99) (386.31, 242.54) (378.01, 242.54)      /F123 of	<|special_separator|>
(391.06, 233.99) (410.97, 233.99) (410.97, 242.54) (391.06, 242.54)      /F123 three	<|special_separator|>
(415.71, 233.99) (442.84, 233.99) (442.84, 242.54) (415.71, 242.54)      /F123 inputs:	<|special_separator|>
(447.58, 233.99) (498.49, 233.99) (498.49, 242.54) (447.58, 242.54)      /F123 T1-weighted	<|special_separator|>
(503.24, 233.99) (523.43, 233.99) (523.43, 242.54) (503.24, 242.54)      /F123 (T1),	<|special_separator|>
(528.17, 233.99) (563.03, 233.99) (563.03, 242.54) (528.17, 242.54)      /F123 contrast-	<|special_separator|>
(311.97, 222.03) (482.77, 222.03) (482.77, 230.59) (311.97, 230.59)      /F123 enhanced T1 (T1C), and fluid-attenuated	<|special_separator|>
(487.37, 222.03) (523.90, 222.03) (523.90, 230.59) (487.37, 230.59)      /F123 inversion	<|special_separator|>
(528.48, 222.03) (563.03, 222.03) (563.03, 230.59) (528.48, 230.59)      /F123 recovery	<|special_separator|>
(311.97, 210.08) (347.39, 210.08) (347.39, 218.63) (311.97, 218.63)      /F123 (FLAIR)	<|special_separator|>
(352.94, 210.08) (383.65, 210.08) (383.65, 218.63) (352.94, 218.63)      /F123 images.	<|special_separator|>
(389.21, 210.08) (404.70, 210.08) (404.70, 218.63) (389.21, 218.63)      /F123 The	<|special_separator|>
(410.25, 210.08) (467.25, 210.08) (467.25, 218.63) (410.25, 218.63)      /F123 corresponding	<|special_separator|>
(472.81, 210.08) (510.44, 210.08) (510.44, 218.63) (472.81, 218.63)      /F123 treatment	<|special_separator|>
(515.99, 210.08) (563.03, 210.08) (563.03, 218.63) (515.99, 218.63)      /F123 information	<|special_separator|>
(311.97, 198.12) (318.62, 198.12) (318.62, 206.68) (311.97, 206.68)      /F123 is	<|special_separator|>
(324.13, 198.12) (370.05, 198.12) (370.05, 206.68) (324.13, 206.68)      /F123 represented	<|special_separator|>
(375.54, 198.12) (383.84, 198.12) (383.84, 206.68) (375.54, 206.68)      /F123 as	<|special_separator|>
(389.35, 190.63) (394.78, 190.63) (394.78, 207.91) (389.35, 207.91)       /F30 T	<|special_separator|>
(403.82, 198.29) (411.57, 198.29) (411.57, 206.99) (403.82, 206.99)       /F24 =	<|special_separator|>
(418.07, 190.63) (423.06, 190.63) (423.06, 207.91) (418.07, 207.91)       /F30 {	<|special_separator|>
(423.06, 198.31) (428.18, 198.31) (428.18, 207.07) (423.06, 207.07)      /F112 τ	<|special_separator|>
(428.18, 197.37) (432.15, 197.37) (432.15, 203.46) (428.18, 203.46)       /F23 1	<|special_separator|>
(432.64, 198.29) (435.41, 198.29) (435.41, 206.99) (432.64, 206.99)       /F27 ,	<|special_separator|>
(437.07, 198.31) (442.19, 198.31) (442.19, 207.07) (437.07, 207.07)      /F112 τ	<|special_separator|>
(442.19, 197.37) (446.17, 197.37) (446.17, 203.46) (442.19, 203.46)       /F23 2	<|special_separator|>
(446.66, 198.29) (467.15, 198.29) (467.15, 206.99) (446.66, 206.99)       /F27 , . . . ,	<|special_separator|>
(468.80, 198.31) (473.92, 198.31) (473.92, 207.07) (468.80, 207.07)      /F112 τ	<|special_separator|>
(473.92, 197.37) (476.44, 197.37) (476.44, 203.46) (473.92, 203.46)       /F26 l	<|special_separator|>
(476.98, 198.29) (497.46, 198.29) (497.46, 206.99) (476.98, 206.99)       /F27 , . . . ,	<|special_separator|>
(499.12, 198.31) (504.24, 198.31) (504.24, 207.07) (499.12, 207.07)      /F112 τ	<|special_separator|>
(504.24, 197.37) (509.70, 197.37) (509.70, 203.46) (504.24, 203.46)       /F26 L	<|special_separator|>
(510.20, 190.63) (515.18, 190.63) (515.18, 207.91) (510.20, 207.91)       /F30 }	<|special_separator|>
(515.18, 198.12) (517.68, 198.12) (517.68, 206.68) (515.18, 206.68)      /F123 ,	<|special_separator|>
(523.18, 198.12) (563.03, 198.12) (563.03, 206.68) (523.18, 206.68)      /F123 indicating	<|special_separator|>
(311.97, 186.17) (563.03, 186.17) (563.03, 194.72) (311.97, 194.72)      /F123 the treatment distribution, with the associated treatment days	<|special_separator|>
(311.97, 174.21) (341.30, 174.21) (341.30, 182.77) (311.97, 182.77)      /F123 defined	<|special_separator|>
(346.27, 174.21) (354.57, 174.21) (354.57, 182.77) (346.27, 182.77)      /F123 as	<|special_separator|>
(359.55, 166.72) (367.24, 166.72) (367.24, 184.00) (359.55, 184.00)       /F30 D	<|special_separator|>
(373.03, 174.38) (380.78, 174.38) (380.78, 183.08) (373.03, 183.08)       /F24 =	<|special_separator|>
(386.31, 166.72) (391.29, 166.72) (391.29, 184.00) (386.31, 184.00)       /F30 {	<|special_separator|>
(391.29, 174.38) (396.47, 174.38) (396.47, 183.08) (391.29, 183.08)       /F27 d	<|special_separator|>
(396.47, 173.45) (400.44, 173.45) (400.44, 179.55) (396.47, 179.55)       /F23 1	<|special_separator|>
(400.94, 174.38) (410.56, 174.38) (410.56, 183.08) (400.94, 183.08)       /F27 , d	<|special_separator|>
(410.55, 173.45) (414.53, 173.45) (414.53, 179.55) (410.55, 179.55)       /F23 2	<|special_separator|>
(415.02, 174.38) (442.35, 174.38) (442.35, 183.08) (415.02, 183.08)       /F27 , . . . , d	<|special_separator|>
(442.35, 173.45) (444.87, 173.45) (444.87, 179.55) (442.35, 179.55)       /F26 l	<|special_separator|>
(445.41, 174.38) (472.73, 174.38) (472.73, 183.08) (445.41, 183.08)       /F27 , . . . , d	<|special_separator|>
(472.73, 173.45) (478.20, 173.45) (478.20, 179.55) (472.73, 179.55)       /F26 L	<|special_separator|>
(478.69, 166.72) (483.68, 166.72) (483.68, 184.00) (478.69, 184.00)       /F30 }	<|special_separator|>
(493.64, 166.72) (499.17, 166.72) (499.17, 184.00) (493.64, 184.00)       /F30 ∀	<|special_separator|>
(509.14, 174.38) (514.32, 174.38) (514.32, 183.08) (509.14, 183.08)       /F27 d	<|special_separator|>
(519.84, 166.72) (526.49, 166.72) (526.49, 184.00) (519.84, 184.00)       /F30 ∈	<|special_separator|>
(532.01, 176.28) (539.20, 176.28) (539.20, 180.90) (532.01, 180.90)      /F110 N	<|special_separator|>
(539.20, 173.45) (543.17, 173.45) (543.17, 179.55) (539.20, 179.55)       /F23 0	<|special_separator|>
(548.65, 174.21) (563.03, 174.21) (563.03, 182.77) (548.65, 182.77)      /F123 and	<|special_separator|>
(311.97, 162.42) (316.95, 162.42) (316.95, 171.13) (311.97, 171.13)       /F24 0	<|special_separator|>
(322.13, 154.76) (329.88, 154.76) (329.88, 172.04) (322.13, 172.04)       /F30 ≤	<|special_separator|>
(335.05, 162.42) (340.24, 162.42) (340.24, 171.13) (335.05, 171.13)       /F27 d	<|special_separator|>
(340.24, 161.50) (342.76, 161.50) (342.76, 167.59) (340.24, 167.59)       /F26 l	<|special_separator|>
(342.80, 156.20) (349.02, 156.20) (349.02, 168.28) (342.80, 168.28)       /F29 -	<|special_separator|>
(349.02, 161.50) (353.00, 161.50) (353.00, 167.59) (349.02, 167.59)       /F23 1	<|special_separator|>
(358.67, 162.42) (376.77, 162.42) (376.77, 171.13) (358.67, 171.13)       /F27 < d	<|special_separator|>
(376.77, 161.50) (379.30, 161.50) (379.30, 167.59) (376.77, 167.59)       /F26 l	<|special_separator|>
(379.83, 162.26) (382.32, 162.26) (382.32, 170.81) (379.83, 170.81)      /F123 .	<|special_separator|>
(387.11, 162.26) (404.82, 162.26) (404.82, 170.81) (387.11, 170.81)      /F123 This	<|special_separator|>
(409.61, 162.26) (472.40, 162.26) (472.40, 170.81) (409.61, 170.81)      /F123 work considers	<|special_separator|>
(477.19, 162.26) (534.44, 162.26) (534.44, 170.81) (477.19, 170.81)      /F123 two treatment	<|special_separator|>
(539.24, 162.26) (563.03, 162.26) (563.03, 170.81) (539.24, 170.81)      /F123 types:	<|special_separator|>
(311.97, 150.30) (563.03, 150.30) (563.03, 158.85) (311.97, 158.85)      /F123 chemoradiation (CRT) and temozolomide (TMZ), specified as	<|special_separator|>
(311.97, 138.53) (317.09, 138.53) (317.09, 147.30) (311.97, 147.30)      /F112 τ	<|special_separator|>
(319.86, 130.85) (334.25, 130.85) (334.25, 148.13) (319.86, 148.13)       /F30 ∈ {	<|special_separator|>
(334.25, 138.51) (339.23, 138.51) (339.23, 147.22) (334.25, 147.22)       /F24 1	<|special_separator|>
(339.23, 138.51) (342.00, 138.51) (342.00, 147.22) (339.23, 147.22)       /F27 ,	<|special_separator|>
(343.66, 138.51) (348.64, 138.51) (348.64, 147.22) (343.66, 147.22)       /F24 2	<|special_separator|>
(348.64, 130.85) (372.34, 130.85) (372.34, 148.13) (348.64, 148.13)       /F30 } ∼ T	<|special_separator|>
(374.87, 138.35) (377.36, 138.35) (377.36, 146.90) (374.87, 146.90)      /F123 .	<|special_separator|>
(321.94, 126.15) (378.77, 126.15) (378.77, 134.71) (321.94, 134.71)      /F123 We randomly	<|special_separator|>
(384.38, 126.15) (412.61, 126.15) (412.61, 134.71) (384.38, 134.71)      /F123 sample	<|special_separator|>
(418.23, 126.15) (422.65, 126.15) (422.65, 134.71) (418.23, 134.71)      /F123 a	<|special_separator|>
(428.27, 126.15) (452.62, 126.15) (452.62, 134.71) (428.27, 134.71)      /F123 sorted	<|special_separator|>
(458.22, 126.15) (494.74, 126.15) (494.74, 134.71) (458.22, 134.71)      /F123 sequence	<|special_separator|>
(500.36, 126.15) (508.65, 126.15) (508.65, 134.71) (500.36, 134.71)      /F123 of	<|special_separator|>
(514.26, 126.15) (534.18, 126.15) (534.18, 134.71) (514.26, 134.71)      /F123 three	<|special_separator|>
(539.80, 126.15) (563.03, 126.15) (563.03, 134.71) (539.80, 134.71)      /F123 scalar	<|special_separator|>
(311.97, 114.20) (340.20, 114.20) (340.20, 122.75) (311.97, 122.75)      /F123 indices	<|special_separator|>
(347.09, 114.20) (366.46, 114.20) (366.46, 122.75) (347.09, 122.75)      /F123 from	<|special_separator|>
(373.35, 114.20) (408.87, 114.20) (408.87, 122.75) (373.35, 122.75)      /F123 available	<|special_separator|>
(415.76, 114.20) (463.92, 114.20) (463.92, 122.75) (415.76, 122.75)      /F123 longitudinal	<|special_separator|>
(470.81, 114.20) (496.11, 114.20) (496.11, 122.75) (470.81, 122.75)      /F123 exams	<|special_separator|>
(503.01, 114.20) (511.31, 114.20) (511.31, 122.75) (503.01, 122.75)      /F123 as	<|special_separator|>
(518.20, 114.20) (563.03, 114.20) (563.03, 122.75) (518.20, 122.75)      /F123 conditional	<|special_separator|>
(311.97, 102.24) (344.34, 102.24) (344.34, 110.80) (311.97, 110.80)      /F123 sources,	<|special_separator|>
(348.58, 102.24) (360.75, 102.24) (360.75, 110.80) (348.58, 110.80)      /F123 i.e.	<|special_separator|>
(364.98, 094.75) (371.01, 094.75) (371.01, 112.03) (364.98, 112.03)       /F30 S	<|special_separator|>
(375.90, 102.41) (383.65, 102.41) (383.65, 111.11) (375.90, 111.11)       /F24 =	<|special_separator|>
(387.80, 094.75) (392.78, 094.75) (392.78, 112.03) (387.80, 112.03)       /F30 {	<|special_separator|>
(392.78, 102.41) (397.45, 102.41) (397.45, 111.11) (392.78, 111.11)       /F27 s	<|special_separator|>
(397.45, 101.48) (401.42, 101.48) (401.42, 107.58) (397.45, 107.58)       /F23 1	<|special_separator|>
(401.92, 102.41) (411.02, 102.41) (411.02, 111.11) (401.92, 111.11)       /F27 , s	<|special_separator|>
(411.01, 101.48) (414.99, 101.48) (414.99, 107.58) (411.01, 107.58)       /F23 2	<|special_separator|>
(415.48, 102.41) (424.58, 102.41) (424.58, 111.11) (415.48, 111.11)       /F27 , s	<|special_separator|>
(424.58, 101.48) (428.55, 101.48) (428.55, 107.58) (424.58, 107.58)       /F23 3	<|special_separator|>
(429.05, 094.75) (434.03, 094.75) (434.03, 112.03) (429.05, 112.03)       /F30 }	<|special_separator|>
(434.03, 102.24) (436.52, 102.24) (436.52, 110.80) (434.03, 110.80)      /F123 ,	<|special_separator|>
(440.76, 102.24) (478.19, 102.24) (478.19, 110.80) (440.76, 110.80)      /F123 such that	<|special_separator|>
(482.42, 102.41) (487.09, 102.41) (487.09, 111.11) (482.42, 111.11)       /F27 s	<|special_separator|>
(487.09, 101.48) (489.91, 101.48) (489.91, 107.58) (487.09, 107.58)       /F26 i	<|special_separator|>
(494.55, 094.75) (501.19, 094.75) (501.19, 112.03) (494.55, 112.03)       /F30 ∈	<|special_separator|>
(505.34, 102.41) (513.09, 102.41) (513.09, 111.11) (505.34, 111.11)       /F24 [1	<|special_separator|>
(513.09, 102.41) (542.00, 102.41) (542.00, 111.11) (513.09, 111.11)       /F27 , . . . , L	<|special_separator|>
(544.77, 094.75) (552.52, 094.75) (552.52, 112.03) (544.77, 112.03)       /F30 -	<|special_separator|>
(555.28, 102.41) (563.03, 102.41) (563.03, 111.11) (555.28, 111.11)       /F24 1]	<|special_separator|>
(311.97, 090.29) (326.36, 090.29) (326.36, 098.84) (311.97, 098.84)      /F123 and	<|special_separator|>
(331.53, 090.45) (336.20, 090.45) (336.20, 099.16) (331.53, 099.16)       /F27 s	<|special_separator|>
(336.20, 089.53) (339.02, 089.53) (339.02, 095.62) (336.20, 095.62)       /F26 i	<|special_separator|>
(345.41, 082.79) (353.16, 082.79) (353.16, 100.08) (345.41, 100.08)       /F30 ≤	<|special_separator|>
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