SUMMARY ORDER

Petitioner Xiao He Chen, a Chinese citizen, petitions for review of the BIA’s August 14, 2002 order summarily affirming an IJ’s denial of her application for asylum *403and withholding of removal based on China’s restrictive family planning policies. We assume the parties’ familiarity with the facts and the record of prior proceedings, which we reference only as necessary to explain our decision.

1. Incomplete Record on Appeal

Chen’s argument that her case should be remanded because the government failed to include a complete record on appeal is moot. The government investigated this claim and filed a supplemental administrative record on October 1, 2004, before filing its own brief. Chen did not file a reply brief or complain that the supplemented record was inadequate. Thus, this court was able to review her claim on the complete record.

2. Unexhausted Claims

Petitioner seeks review on several issues that she did not raise before the BIA: (1) the IJ improperly based his adverse credibility finding on alleged inconsistencies in petitioner’s testimony before two different IJs, (2) the IJ improperly required corroborating evidence of petitioner’s ill health, (3) the IJ improperly excluded petitioner’s supplemental statement, and (4) the IJ failed to consider petitioner’s three children in assessing her claim that she would face future persecution on return to China. Although some of these arguments raise concerns, we are jurisdictionally barred from reviewing them at this time because Chen failed to exhaust her administrative remedies. See 8 U.S.C. § 1252(d)(1) (2000); Theodoropoulos v. INS, 358 F.3d 162, 168-74 (2d Cir. 2004); Cervantes-Ascencio v. INS, 326 F.3d 83, 87 (2d Cir. 2003). The same defect precludes our review of petitioner’s claim for relief under the Convention Against Torture. See 8 U.S.C. § 1252(d)(1); Foster v. INS, 376 F.3d 75, 77 (2d Cir. 2004). We do not, however, foreclose the BIA or IJ from giving these issues further consideration on remand.

3. Exhausted Claims

Petitioner raises two issues in support of her petition that were properly exhausted before the BIA: (1) the IJ’s decision to afford no weight to the notarial birth and marriage certificates that she submitted to corroborate her claim for relief, and (2) the IJ’s dismissal of her account of interactions with Chinese family planning officials as implausible.

a. Corroborative Documentary Evidence

In a September 9, 1999 oral decision, the IJ stated that he gave no weight to the notarial birth and marriage certificates offered into evidence by Chen because they were not contemporaneously obtained and the circumstances of their issuance were unclear. In fact, petitioner had testified that the documents were brought to her from China by friends, although she did not know how they had been obtained. She stated that she herself had brought no documents when she fled China. She had left her original marriage certificate behind because she did not think it would be important. The IJ did not assess the credibility of Chen’s explanation for why she did not have the original certificates; he noted only that petitioner should have provided corroborative evidence in the form of affidavits from family members in China who allegedly had witnessed her interactions with family planning officials.

This court has ruled that, when an IJ requires further corroboration of a petitioner’s account, he “should explain specifically, either in [his] decision or otherwise in the record: (1) why it is reasonable under the BIA’s standards to expect such corroboration; and (2) why [petitioner’s] proffered explanations for the lack of such *404corroboration are insufficient.” Diallo v. INS, 232 F.3d 279, 290 (2d Cir. 2000); accord Cao He Lin v. United States Dep’t of Justice, 428 F.3d 391 (2d Cir. 2005) (“[A]n IJ has an obligation to ensure that documentation is available before relying on the applicant’s failure to produce it.”); Abankwah v. INS, 185 F.3d 18, 26 (2d Cir. 1999) (“[I]t must be acknowledged that a genuine refugee does not flee her native country armed with affidavits, expert witnesses, and extensive documentation.”). In this case, the IJ did neither. He did not state why it was reasonable to expect additional corroboration for Chen’s testimony, nor did he explain why Chen’s explanations for the lack of contemporaneous documentary corroboration were insufficient. This is not to suggest that no such explanations could be given. But we are not free to hypothesize reasons not stated by the IJ. Secaida-Rosales v. INS, 331 F.3d 297, 305 (2d Cir. 2003). We cannot affirm an IJ’s conclusions if they are based on “bald speculation,” Zhang v. United States INS, 386 F.3d 66, 74 (2d Cir. 2004), including bald speculation “as to the existence or nature” of Chinese procedures for obtaining birth and marriage certificates, Cao He Lin v. United States Dep’t of Justice, 428 F.3d 391. Accordingly, we remand for further proceedings so that the IJ can either provide the specific reasons required by Diallo for demanding more corroboration from Chen, or give due consideration to the corroborative documentary evidence that she did provide.

b. Implausibility

Chen testified that family planning officials allowed her to bear her second child because her mother-in-law told the officials that she was ill and that her life would be endangered by an abortion. The IJ dismissed this explanation as implausible, stating that it “made no sense” to him that officials would capture and then release petitioner. Additionally, the IJ concluded without explanation that it was implausible that Chen had been able to bear her second child despite her alleged ill health during pregnancy, and that she could have given birth to her third child while in hiding from family planning officials. While some conduct may be so bizarre or contrary to core human experience as to be “inherently improbable,” Zhang v. United States INS, 386 F.3d at 74 (internal quotation marks omitted), this court has ruled that an IJ may not rely on mere “speculation or conjecture” in reaching such a conclusion, Secaida-Rosales v. INS, 331 F.3d at 307 (internal quotation marks omitted); accord Zhang v. United States INS, 386 F.3d at 74. An IJ cannot find improbability based on nothing more than his “own unsupported opinion as to how an authoritarian government operates.” Secaida-Rosales v. INS, 331 F.3d at 309 (internal quotation marks omitted). His conclusion must find some evidentiary support in the record. See id. at 307. In this case, the IJ neither pointed to any evidence nor offered any specific cogent reasons to support his conclusion that Chen’s account of her experiences was implausible. Under these circumstances, we are obliged to conclude that the IJ’s decision was based on “flawed reasoning” rather than the requisite “substantial evidence.” Cao v. United States Dep’t of Justice, 428 F.3d 391; see also Secaida-Rosales v. INS, 331 F.3d at 307. We remand this case so that the IJ can either (1) support his implausibility conclusion with cogent reasons based on record evidence or (2) credit Chen’s account.

We GRANT the petition for review, and hereby VACATE and REMAND the BIA’s order with instructions to remand this matter to the IJ for proceedings consistent with this order.